Multiplication using recursion Mar 17, 2025 · To find the product of two numbers x and y using recursion, you can use the following approach: Base Case: If y=0, return 0 (since any number multiplied by 0 is 0). We're supposed to use recursion to solve this problem, so i tried just adding n with itself, m number of times. It is a programming technique that naturally implements the divide-and-conquer problem solving methodology. You can only use subtraction and addition for your calculation. 1 Recursion Recursion in computer science and mathematics refers to the idea of describing the solution of a problem in terms of solutions to easier instances of the same problem. This allows the function to repeatedly call itself, but provides the condition on which to stop. In order to become competent and confident with writing recursive algorithms, use recursion for multiplication. the prototyping of the fu Karatsuba multiplication of az+b and cz+d (boxed), and 1234 and 567 with z=100. This function has to multiply two numbers without multiplication operation. I managed to do that using recursion, but stuck at the point where I wa This video explains all the concepts of matrix chain multiplication using recursion. The multiplication of two numbers can be found by the repeated addition method. Java Program to Multiply Two Numbers Using Recursion Multiplying two numbers means finding the product of two numbers. When I was a lecturer, teaching recursive functions was both fun and annoying because most students were unable to understand it for the first time. c_11 = c_11 + a_11 · b_11 return // This video explains all the concepts of matrix chain multiplication using recursion. Assume A; B 2 Rn n and C = AB, where n is a power of two. Aug 17, 2020 · Here we determine how to multiply x and y using recursion. x and y are the two matrices you're multiplying together, which you store in result. I think my problem is with using recursion itself. (A), (B) and (C) show recursion with z=10 to obtain intermediate values. I found this example in my course page for calculating the multiplication of two numbers recursively : Thus our method for multiplying n-bit numbers starts by making recursive calls to multiply these four pairs of n=2-bit numbers (four subproblems of half the size), and then evaluates the preceding expression in O(n) time. Dec 5, 2010 · I am looking for a way to code a program which will multiply an integer to an exponent using only a recursion loop. Here, we will calculate the product of two numbers using various methods. In this section, we will learn how to multiply two numbers without using the arithmetic operator (*) in Java. But while using recursion, programmers need to be careful to define an exit condition from the function, otherwise it will go into an infinite loop. I have a very limited understanding of recursion, but have been able to code some Nov 26, 2013 · Can somebody please explain how this recursive function is doing? I'm struggling to understand how you can multiply numbers by using just + static int Multiply(int x, int y) { In this video, you’ll learn how to print the multiplication table of any number using recursion in Java. This is the best place to expand your knowledge and get prepared for your next interview. Write a C program to recursively compute the product of two matrices and print the resultant matrix. If b is 0, return 0 (base case). Dec 22, 2023 · In Recursive Matrix Multiplication, we implement three loops of Iteration through recursive calls. * Note: * You CANNOT use the mult or mul instructions. Jan 4, 2016 · 2 Okay, let's understand conceptually what you want to achieve with recursion. Write a C program to perform matrix multiplication using dynamic memory allocation for the matrices. We can write the Python Program for multiplication of two matrices using various methods. 2 We write A and B as block matrices, Oct 9, 2019 · I`m new to Python. Test Data : Input number of rows for the first matrix : 2 Input number of columns for the first matrix : 1 Input number of rows for the second matrix : 1 Input number of columns for the second matrix : 2 Input elements in the first matrix : Oct 4, 2021 · Karatsuba multiplication is a fast, recursive algorithm discovered by Anatoly Karatsuba in 1960 that can multiply integers using addition, subtraction, and a pre-computed multiplication table of all products from single-digit numbers. Jun 7, 2024 · The Naive Recursive Approach for Matrix Chain Multiplication involves solving the problem recursively by considering all possible partition points in the chain of matrices. Jun 15, 2017 · A recursive, divide-and-conquer algorithm is then: For multiplying two matrices of size n x n, we make 8 recursive calls above, each on a matrix/subproblem with size n/2 x n/2. 1. Jan 14, 2023 · So I was searching for a way to print multiplication table using recursion and all the solution I came across were to use 2 parameters. Apr 27, 2022 · Hi Campers, Thanks for your help in advance. rows let c be a new n x n matrix if n == 1 c11 = a11 * b11 else - How to derive recurrence relation?- How to reassemble the result of subproblems to get the result for original problem?- Improving the efficiency of the re I've received an assignment to write a recursive function that receives two integersd from the user: x and y and prints out the multiplication table up to the number x*y. Please subscribe for updates and more videos!Check out my website: www. Now I am learning about recursion. I am limited to using addition/subtraction/negation operators, along with recursion. 16 Zylab 5 - Recursive Procedure CallWrite a MIPS program to compute the product of two 16-bit signed numbers using *recursive procedure calls. e. Jul 23, 2025 · Time complexity of multiplication can be further improved using another Divide and Conquer algorithm, fast Fourier transform. And it behaves such Sep 11, 2023 · The recursive solution (naive) for matrix chain multiplication repeatedly splits the chain at different positions and calculates the cost, returning the minimum number of multiplications needed. Aug 16, 2025 · Learn how to write a C++ program that uses recursion to calculate the product of two numbers without using the multiplication operator. No other operators are allowed. No other opera Nov 3, 2020 · Give a recursive algorithm for computing nxwhenever n is a positive integerand x is an integer, using just addition. , 54). I don't understand the recursion method for multiplying two numbers. Divide and conquer techniques come in when Karatsuba uses recursion to solve subproblems--for example, if multiplication is needed to solve for a a, d d, or e e before those variables can be used to solve the overall x × y x ×y multiplication. Every recursive function must have a base condition that stops the recursion or else the function calls itself infinitely. A recursive function simply means this: a function that has the ability to invoke itself. Instead of directly multiplying a and b, we repeatedly halve b and double a, leveraging the fact that multiplication can be rewritten as repeated addition. def mult(a, b): '''Returns the product of a and b''' # using only add, incr, decr, zero, and recursion #base case if zero(b In the previous article, we have discussed Python Program to Find Subtraction of Two Numbers using Recursion Given two numbers and the task is to find the multiplication of the given two numbers using recursion. Mar 3, 2016 · I am writing a simple code in Java that is using recursion. Check if the first number is less than the second number using the if conditional statement. Dec 15, 2021 · This article will focus on Strassen’s multiplication recursive algorithm for multiplying nxn matrices, which is a little faster than the simple brute-force method. The program takes two numbers and finds the product of two numbers using recursion. , T. Write a C program to multiply two matrices and then transpose the resulting matrix. The problem is not actually to perform the The cache miss rate of recursive matrix multiplication is the same as that of a tiled iterative version, but unlike that algorithm, the recursive algorithm is cache-oblivious: [6] there is no tuning parameter required to get optimal cache performance, and it behaves well in a multiprogramming environment where cache sizes are effectively Sep 19, 2016 · -4 so as homework for a programming class on python we're supposed to multiply to integers (n,m) with each other WITHOUT using the * sign (or another multiplication form). Write a C program to multiply two matrices using recursion. The simplest way to Fibonacci Recursion Computing the value of a Fibonacci number can be implemented using recursion. Nov 11, 2013 · I think this violates the spirit of the question because you're using /, *, and %, which are all in the multiplicative family of operations. Feb 12, 2021 · The original question from CTCI is (Question 8. Mar 7, 2024 · In Python, a common task might be to multiply two numbers, but what if we approached this problem using recursion instead of the standard multiplication operator? The goal is to create a program that, given two integer inputs (e. So I would like to know if there is anyway to do the same thi A recursive procedure is designed using the base case (or base cases) and a recursive case. Note: The numbers can be both positive or negative. The Python interpreter limits the depths of recursion to help avoid infinite recursions, resulting in stack overflows. The Big-O runtime of the Fibonacci function is O (2^N). more Sep 20, 2020 · Here is the source code of the C Program to Multiply two numbers using recursion. Store the result of the recursive function call in variable result. Mar 14, 2022 · I'm designing a recursive algorithm, in order to create a function that compute product of two positive integers. Honestly, I don't know if it's the Aug 1, 2020 · I did a recursive function to calculate x*y with x and y are all integers (x and y >= 0). Display the result of the multiplication. Feb 6, 2018 · In Recursive Matrix Multiplication, we implement three loops of Iteration through recursive calls. Magenta arrows denote multiplication, amber denotes addition, silver denotes subtraction and cyan denotes left shift. The recursive function becomes an infinite loop even with the smallest mistake. Call the recursive multiply(a, b) function: a. Jan 20, 2022 · In this article we will see C Program to find Product of 2 Numbers using Recursion logic with output. using recursion and pointer. Jul 23, 2025 · We will be using the same concept to find the factorial of a number without using asterisk. The function russian_peasant_recursive() handles the logic to check if the current value of a is zero, even, or odd, and returns the final result by recursively calling itself with half of a and double b. Otherwise, return a + multiply(a, b - 1) (recursive case). A recursive function always has a structure using an if. Mar 2, 2024 · This snippet demonstrates Russian Peasant Multiplication using recursion. In this video, get the opportunity to implement a recursive algorithm in Python to Fibonacci Recursion Computing the value of a Fibonacci number can be implemented using recursion. mult_mat(M, 2) will give M * M, therefore, mult_mat(M, 1) just returns M itself. Explanation: For the multiplication two square matrix recursively using Simple Divide and Conquer Method, there are 8 recursive calls performed for high time complexity. Follow the steps below to solve the problem: Take a variable of integer type (here: n) which would store the value of which we're finding the factorial. Using Recursion The idea is that for given two numbers a and b, we can get a×b by adding an integer a exactly b times to the result. it defines a recursive function repeat_multiply_list () which takes the original list, N and M as input and repeatedly calls itself to generate the extended list. Make sure to double-check your code. Jun 9, 2023 · In this article, I will be sharing my method on how to multiply 2 numbers without using the multiplication operator. basic idea: function definition must be & Jun 1, 2018 · I had an interesting interview yesterday where the interviewer asked me a classic question: How can we multiply two numbers in Java without using the * operator. Jul 31, 2025 · Write a C program to multiply two square matrices and then display the sum of each row in the product. Recursive Case: Add x to result and make a recursive call with y as y-1. Jul 25, 2024 · Matrix Chain Multiplication — Dynamic Programming Approach Detailed Analysis (Recursion and Tabulation) Matrix chain multiplication is a classic problem in computer science and mathematics In this tutorial we will create a program in C which will ask the user for a number and then print the multiplication table of that number. To get you going, think about how you would get a single digit from any number, then multiply that digit with the result of calling the function again (with one digit less in its argument). Mar 17, 2023 · Method #3: Using recursion This function takes a list, N and M as input and returns the list after extension and multiplication using recursion. Recursion is basically a form of repetition, and we can understand it by making distinct what it means for a function to be recursive, as compared to how it behaves. May 6, 2024 · Pass the given two numbers as the arguments to recur_mult function. Jun 26, 2021 · CC 13. Input format: m and n (in different lines) Sample Input: 3 5 Sample Output: 15 This video is based on Python Programming for Computer Science and Engineering students. 16 Zylab 5 - Recursive Procedure Call (no chatgpt answer please) Write a MIPS program to compute the product of two 16-bit signed numbers using * recursive procedure calls. Then, calculate the product of those numbers using the multiplication operator (*). Learn how to create multiplication tables using different techniques, learn now! Nov 12, 2014 · If you want a recursive solution, then yes there is a shorter way. I know that in recursion we call function inside function. We use 2 D array to represent a matrix and resulting matrix is stored in a different matrix. Karthikeyan , Noor Mahammad Sk. Jul 23, 2025 · We can solve the problem using recursion based on the following facts and observations: Now, for a given chain of n matrices, the first partition can be done in n-1 ways. Write a C program to implement Strassen’s algorithm recursively for matrix multiplication. 8), which is less than O (n^3). The integers are added multiple times to get the final multiplication result. Sep 1, 2023 · Energy efficient multiply-accumulate unit using novel recursive multiplication for error-tolerant applications Skandha Deepsita S. It’s the core logic that invokes the function until a condition. Approach: Since we cannot use any of the given symbols, the only way left is to use recursion, with the fact that x is to be added to x y times. In the multiplication, you have 3 matrices going on. If you This C program using recursion, finds the product of 2 numbers without using the multiplication operator. Feb 26, 2025 · Learn how to implement recursive multiplication in Python with this comprehensive guide. We rst cover a variant of the naive algorithm, formulated in terms of block matrices, and then parallelize it. Learn about python program to multiply two numbers using recursion with examples, get product of two numbers in python using recursion Nov 22, 2024 · Call the recursive multiply(a, b) function: a. My formula is: x * y = 0, if x is equal 0 (x >> 1)*(y << 1), if x i Explore 6 different C programming methods to multiply two numbers, including basic multiplication, functions, pointers, recursion, and more. Mar 11, 2016 · I was reading about recursion in Java. Given an input of index N, the recursive function has two base cases – when the index is zero or 1. Examples: Input : N = 5 , M = 3 Output : 15 Input : N = 5 , M = -3 Output : -15 Input : N = -5 , M = 3 Output : -15 Input : N = -5 , M = -3 Output:15 A recursive solution to the above problem for only positive numbers is already discussed in the Exploring multiplication tackles implementing multiplication recursively without the use of the multiplication operator or loops. Jan 15, 2023 · I can multiply two numbers without using multiplication operator in c. The task is to find the product of the 2 numbers using recursion. In this vi Dec 6, 2022 · I'd like to step thru the algorithm below to see if I understand how it works. This concept applies to de nitions as well as to algorithms or programs. Initialize a variable (here: p) which would serve to be the factorial of n. [1] Idea - Block Matrix Multiplication The idea behind Strassen's algorithm is in the formulation of matrix multiplication as a recursive problem. To multiply a and b, you need to add a to itself b times. Book shows pseudocode for simple divide and conquer matrix multiplication: n = A. How to solve this problem by using recursive and iterative approach. Sep 20, 2025 · This code compares tail recursion and non-tail recursion using two versions of factorial function one with an accumulator (tail-recursive) and one with multiplication after recursive call (non-tail-recursive). GitHub Gist: instantly share code, notes, and snippets. A mathematical operation is performed on a pair of numbers in order to derive a third number called a product. Exploring multiplication tackles implementing multiplication recursively without the use of the multiplication operator or loops. Mar 24, 2025 · The idea is to break multiplication into a series of additions using the Russian Peasant Algorithm. Perform the following multiplication using the Karatsuba method: 1234 × 4321 1234 ×4321. . Sep 19, 2025 · Multiply two numbers without using a multiplication operator or loops Given two integers, multiply them without using the multiplication operator or conditional loops. Recursion for matrix multiplication. Pictorial representation of how a recursive function actually works for factorial example Recursion is when a function calls itself . A simple yet powerful multiplication algorithm Aug 2, 2020 · Contents [hide] 1 The approach and Example: 2 PsuedoCode for multiplication of two numbers using recursion: 3 Code in C: 4 Output: [New] Matrix Chain Multiplication using Dynamic Programming Formula Dynamic Programming Playlist | Interview Questions | Recursion | Tabulation | Striver | C++ | Java | DSA | Placements We will develop a Python program for multiplication of two numbers. What is the Recursive Solution to the Matrix Chain Multiplication Problem? For the recursion based approach, you will follow the below steps: C Recursion Solved Programs C Recursion Solved Programs —> C is a powerful general-purpose programming language. I want to show the product of two numbers that a user will enter. Feb 5, 2020 · Matrix Chain Multiplication using Recursion Given a sequence of matrices, find the most efficient way to multiply these matrices together. You want to multiply a matrix, M, with itself. Here we are using recursive method. 5 on recursion and dynamic programming): Write a recursive function to multiply two positive integers without using the * operator. There is no definite rule for writing recursive functions. No other operators are allowed Nov 1, 2025 · 15. The Karatsuba algorithm is a fast multiplication algorithm for integers. Given two integers M & N, calculate and return their multiplication using recursion. Recursion: Recursion is the process by which a function calls itself directly or indirectly, and the associated function is known […] Oct 19, 2022 · In this article we have seen simple process to multiply two integers using recursion. Create a recursive function to say recur_mult which takes the two numbers as arguments and returns the multiplication of the given two numbers using recursion. You can use addition, subtraction, and bit shifting, but you should minimize the number of those operations. My solution is: Matrix Multiplication in C to calculate the product of two matrices using iterative and recursive methods along with explanations and examples. , a function to call itself. when to switch from recursion to the standard method of multiplication. Oct 17, 2012 · I am reading Introduction to Algorithms by CLRS. Given two integers m & n, calculate and return their multiplication using recursion. Write a C program to print multiplication table using recursion function. Jun 20, 2019 · This is my problem statement. Nov 29, 2016 · The C programming language supports recursion, i. It will include my thought process while solving this problem and step-by-step Master multiplication with our JavaScript Multiplication Table. The Karatsuba method takes the divide and conquer approach by dividing the problem into multiple sub-problems and applies recursion to make the multiplication simpler. *Note:* You CANNOT use the mult or mul instructions. #pythonprogramming , #multiplication , #recursion In the previous article, we have discussed Python Program to Find Sum of Even Numbers Using Recursion in a List/Array Given a number and the task is to print the multiplication table of that number using recursion in python. b. EverythingComputerScience. Hence you have to give a lot of focus while writing recursive functions in python. Oct 11, 2024 · 2 X 10 = 20 Program to Print Multiplication Table using Recursion in Python Below are the ways to print the multiplication table of the given number using recursion in python: Using Recursion (Static Input) Using Recursion (User Input) Method #1: Using Recursion (Static Input) Approach: Give the number as static input and store it in a variable. Multiplication Function in C Recursion Computer Science (compsci112358) 115K subscribers 22 Apr 10, 2022 · Recursive functions play a central role in Haskell, and are used throughout computer science and mathematics generally. The base cases may be used to explicitly define the output of a calculation, or they may be used to signal the end of a recursive process and stop the repeated execution of a procedure. No loops needed — just clean, recursive logic!👨💻 W Level up your coding skills and quickly land a job. Write a multiply function that multiples 2 integers without using * Nov 22, 2024 · Input the second number and store it in variable b. Base case: When the numbers of times x has to be added becomes 0. I'm having problem with the pseudo-code. print("N*i = ", N*i) Mar 7, 2017 · Multiplication using recursion. The time complexity of this algorithm is O (n^ (2. If you are new to programming, C is a good choice to start your programming journey. It's a simple idea, by solving a simpler version of the same problem, until we reach a "base" case Mar 9, 2017 · I saw this interview question and decided to solve using recursion in Java. Recursion: Recursion is the process by which a function calls itself directly or indirectly, and the […] Apr 4, 2024 · In this article we are going to see how we can multiply two numbers using recursion by Java programming language. Jul 11, 2025 · Given two numbers N and M. For a recursive function that takes a and b for arguments: each function call will add a to the result of the recursive call; and on each recursive call 'b' is decremented; the recursion stops when b is zero. c_11 = c_11 + a_11 · b_11 return // Jul 13, 2021 · Here, we are going to learn how to perform matrix multiplication operation using recursion in C programming language? Multiplication of two numbers did not need a recursive function, did not even need an iterative function! Factorial was a little more intuitive to implement with recursion We translated a mathematical equation that told us the structure MOST problems do not need recursion to solve them If iteration is more intuitive for you then solve them Dec 10, 2018 · Here, we are implementing a C++ program to obtain multiplication recursively. The following C program, using recursion, performs Matrix multiplication of two matrices and displays the result. For example, inductive de nitions can be thought of as a recursive de nitions since they de ne more complex instances of a concept in terms In this video, you’ll learn how to print the multiplication table of any number using recursion in Java. Jul 21, 2020 · Definition of addition and multiplication on $ℕ$ using recursion Ask Question Asked 5 years, 4 months ago Modified 5 years, 4 months ago Dec 1, 2020 · Given two positive numbers, write a C program to multiply two numbers without using * multiplication operator. , 6 and 9), utilizes recursive calls to return the product (e. About Given two integers M & N, calculate and return their multiplication using recursion. It is fast, portable and available in all platforms. g. Feb 5, 2015 · Using recursion in multiply Asked 10 years, 2 months ago Modified 10 years, 2 months ago Viewed 800 times Here is a C program to print multiplication table using for loop, while loop, do while loop, recursion and function, along with explanation and examples. To multiply x and y, recursively add x y times. The recursive matrix multiplication algorithm recursively multiplies the (N/2) x (N/2) matrices and combines them using the equations for multiplying 2 x 2 matrices Nov 1, 2025 · Write a C program to multiply two square matrices using recursion with divide-and-conquer. Is that so? In the Challenge Replace Loops using Recursion, it is established that: multiply(arr, n) == multiply(arr, n - 1) * arr[n - 1] I can´t understand that. I can't figure out how does this function work. function multiply(arr, n) I think “arr” and “n” are The aim of this project was to determine, experimentally, where to set the "breakpoint" of Strassen's algorithm -- i. Please help 12. In reality, both methods "weigh" the same - so, to save memory, I leave out the code. Our recursive Tower of Hanoi algorithm is trivially correct whenn= 0. Oct 20, 2018 · Given that multiplication is repeated addition of a b times, you can establish a base case of b == 0 and recursively add a, incrementing or decrementing b (depending on b 's sign) until it reaches 0. Submitted by Indrajeet Das, on December 10, 2018 Given two integers m and n, calculate and return their multiplication using recursion. Recursive functions have always been tricky for me. Jul 23, 2025 · By making use of recursion, we can multiply two integers with the given constraints. Write a C program to multiply a matrix by a vector recursively. We will give two numbers num1 and num2. Explore various methods, including basic recursive multiplication, optimized techniques using bitwise operations, and tail recursion. 1 - Data Structures and AlgorithmsDate: June 26, 2021Topic: Recursion[Midterm Exam] 8. Oct 5, 2012 · If we do test to see if one side is zero, each time the recursive call to multiply is made, the code must evaluate the expression; however, if we do not test for equals zero, then the code adds a bunch of zeros together n number of times. Sep 14, 2025 · Now, look at the recursive solution to solve the Matrix Chain Multiplication Problem. You can get rid of the 2*z using z+z, and use bitwise operations &1 and >>1 for the even/odd check and division by 2, respectively, but the prof might still object that they're not in the addition family. else statement. print_table (number, multiplier, limit) recursionly prints the multiplication result for number up to the limit. We will soon be discussing fast Fourier transform as a separate post. com Apr 10, 2022 · Recursive functions play a central role in Haskell, and are used throughout computer science and mathematics generally. Multiplication Function in C Recursion Computer Science (compsci112358) 115K subscribers 22 use recursion to multiply 2 integer numbers. Matrix Multiplication Recursion Variants Write a C program to multiply two matrices using recursion. This is Jul 12, 2025 · Recursive call: If the base case is not met, then print its multiplication table for that value and then call the function for next iteration. Overview: Matrix multiplication is based on a divide and conquer-based approach. Let’s see the program how we you multiply two numbers using recursion. Jul 20, 2022 · In recursion, we don’t use loops like for loop or while loop. The inner most Recursive call of multiplyMatrix () is to iterate k (col1 or row2). It can use only i Jul 23, 2025 · Time Complexity: O (N3 ) Auxiliary Space: O (N2) ignoring recursion stack space Java Program for Matrix Chain Multiplication using Dynamic Programming (Tabulation): In iterative approach, we initially need to find the number of multiplications required to multiply two adjacent matrices. For anyn1, the Recursion Fairy correctly moves the top n1 disks (more formally, the Inductive Hypothesis implies that our recursive algorithm correctly moves the topn1 disks) so our algorithm is correct. Start iterating from n to 1. In this example, you will learn about C program to multiply two numbers without using multiplication operator (*) i. Given the multiplicand (md) and multiplier (m) as inputs, write the main and recursion functions to compute the product (p) using the Aug 17, 2020 · Strassen algorithm is a recursive method for matrix multiplication where we divide the matrix into 4 sub-matrices of dimensions n/2 x n/2 in each recursive step. MATRIX-MULTIPLY-RECURSIVE(A, B, C, n) if n == 1 // Base case. This video covers everything you need for solving this problem. Oct 26, 2017 · C Programming - Matrix Chain Multiplication - Dynamic Programming MCM is an optimization problem that can be solved using dynamic programming. Ø Recursion is an important and powerful tool in problem solving and programming. if i understood right, recursion is a function that can continuously feed itself until reaches the base case established. Given the multiplicand (md) and multiplier (m) as inputs, write the main and recursion functions to compute the product (p) using the shift and add Question: 12. Thanks for visiting my blog! Sep 19, 2015 · I need to write the function mult( n, m ) that should output the product of the two integers n and m. The recursive function returns the sum of the index minus 1 and the index minus 2. And it behaves such Jun 7, 2013 · I don't really know what you're looking for (this doesn't use strings to store numbers), but this uses recursion to add a number to itself a certain number of times (multiplication) using recursion for counting how many iterations are left. qcerfzt lldsvo cxmgp kqs wfgyno hitsgehc jalm stdmif vqeq ajiza wnisbike numg owfx vedlg jup