# Print k numbers where all pairs are divisible by m

Given an integer array and two numbers k and m. Print k numbers from the array, such that difference between any two pairs is divisible by m. If there are no k numbers, then print -1.

**Examples:**

Input: arr[] = {1, 8, 4} k = 2 m = 3 Output: 1 4 Explanation: Difference between 1 and 4 is divisible by 3. Input: arr[] = {1, 8, 4} k = 3 m = 3 Output: -1 Explanation: there are only two numbers whose difference is divisible by m, but k is three here which is not possible, hence we print -1.

A **naive approach ** is be to iterate for every element and check with all other elements, and if the count of numbers whose difference is divisible by m is greater then equal to k, then we print those k numbers by again iterating. But this won’t be efficient enough as it runs two nested loops.

Time complexity: O(n * n)

Auxiliary space: O(1)

An **efficient approach** is apply a mathematical approach, where we know if (x-y) % m is equal to x%m – y%m. So if we can store all the numbers who leave the same remainder when divided by m,

And if the count of numbers which leaves the same remainder is more than k or equal to k, then we have our answer as all those numbers who leave the same remainder.

Below is the implementation of the above approach

## C++

`// CPP program to find a list of k elements from ` `// an array such that difference between all of ` `// them is divisible by m. ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// function to generate k numbers whose difference ` `// is divisible by m ` `void` `print_result(` `int` `a[], ` `int` `n, ` `int` `k, ` `int` `m) ` `{ ` ` ` `// Using an adjacency list like representation ` ` ` `// to store numbers that lead to same ` ` ` `// remainder. ` ` ` `vector<` `int` `> v[m]; ` ` ` ` ` `for` `(` `int` `i = 0; i < n; i++) { ` ` ` ` ` `// stores the modulus when divided ` ` ` `// by m ` ` ` `int` `rem = a[i] % m; ` ` ` ` ` `v[rem].push_back(a[i]); ` ` ` ` ` `// If we found k elements which ` ` ` `// have same remainder. ` ` ` `if` `(v[rem].size() == k) ` ` ` `{ ` ` ` `for` `(` `int` `j = 0; j < k; j++) ` ` ` `cout << v[rem][j] << ` `" "` `; ` ` ` `return` `; ` ` ` `} ` ` ` `} ` ` ` ` ` `// If we could not find k elements ` ` ` `cout << ` `"-1"` `; ` `} ` ` ` `// driver program to test the above function ` `int` `main() ` `{ ` ` ` `int` `a[] = { 1, 8, 4 }; ` ` ` `int` `n = ` `sizeof` `(a) / ` `sizeof` `(a[0]); ` ` ` `print_result(a, n, 2, 3); ` ` ` `return` `0; ` `} ` |

*chevron_right*

*filter_none*

## Java

`// Java program to find a list of k elements from ` `// an array such that difference between all of ` `// them is divisible by m. ` `import` `java.util.*; ` `class` `GFG ` `{ ` ` ` `// function to generate k numbers whose difference ` `// is divisible by m ` `static` `void` `print_result(` `int` `a[], ` `int` `n, ` ` ` `int` `k, ` `int` `m) ` `{ ` ` ` `// Using an adjacency list like representation ` ` ` `// to store numbers that lead to same ` ` ` `// remainder. ` ` ` `Vector<Vector<Integer>> v = ` `new` `Vector<Vector<Integer>>(m); ` ` ` `for` `(` `int` `i = ` `0` `; i < m; i++) ` ` ` `v.add(` `new` `Vector<Integer>()); ` ` ` ` ` `for` `(` `int` `i = ` `0` `; i < n; i++) ` ` ` `{ ` ` ` ` ` `// stores the modulus when divided ` ` ` `// by m ` ` ` `int` `rem = a[i] % m; ` ` ` ` ` `v.get(rem).add(a[i]); ` ` ` ` ` `// If we found k elements which ` ` ` `// have same remainder. ` ` ` `if` `(v.get(rem).size() == k) ` ` ` `{ ` ` ` `for` `(` `int` `j = ` `0` `; j < k; j++) ` ` ` `System.out.print(v.get(rem).get(j) + ` `" "` `); ` ` ` `return` `; ` ` ` `} ` ` ` `} ` ` ` ` ` `// If we could not find k elements ` ` ` `System.out.print(` `"-1"` `); ` `} ` ` ` `// Driver Code ` `public` `static` `void` `main(String[] args) ` `{ ` ` ` `int` `a[] = { ` `1` `, ` `8` `, ` `4` `}; ` ` ` `int` `n = a.length; ` ` ` `print_result(a, n, ` `2` `, ` `3` `); ` `} ` `} ` ` ` `// This code is contributed by 29AjayKumar ` |

*chevron_right*

*filter_none*

## Python3

`# Python3 program to find a list of k elements from ` `# an array such that difference between all of ` `# them is divisible by m. ` ` ` `# function to generate k numbers whose difference ` `# is divisible by m ` `def` `print_result(a, n, k, m): ` ` ` ` ` `# Using an adjacency list like representation ` ` ` `# to store numbers that lead to same ` ` ` `# remainder. ` ` ` `v ` `=` `[[] ` `for` `i ` `in` `range` `(m)] ` ` ` ` ` `for` `i ` `in` `range` `(` `0` `, n): ` ` ` ` ` `# stores the modulus when divided ` ` ` `# by m ` ` ` `rem ` `=` `a[i] ` `%` `m ` ` ` ` ` `v[rem].append(a[i]) ` ` ` ` ` `# If we found k elements which ` ` ` `# have same remainder. ` ` ` `if` `(` `len` `(v[rem]) ` `=` `=` `k): ` ` ` ` ` `for` `j ` `in` `range` `(` `0` `, k): ` ` ` `print` `(v[rem][j], end` `=` `" "` `) ` ` ` `return` ` ` ` ` `# If we could not find k elements ` ` ` `print` `(` `-` `1` `) ` ` ` `# driver program to test the above function ` `if` `__name__` `=` `=` `'__main__'` `: ` ` ` `a ` `=` `[` `1` `, ` `8` `, ` `4` `] ` ` ` `n ` `=` `len` `(a) ` ` ` `print_result(a, n, ` `2` `, ` `3` `) ` ` ` `# This code is contributed by ` `# Sanjit_Prasad ` |

*chevron_right*

*filter_none*

## C#

`// C# program to find a list of k elements from ` `// an array such that difference between all of ` `// them is divisible by m. ` `using` `System; ` `using` `System.Collections.Generic; ` ` ` `class` `GFG ` `{ ` ` ` `// function to generate k numbers whose difference ` `// is divisible by m ` `static` `void` `print_result(` `int` `[]a, ` `int` `n, ` ` ` `int` `k, ` `int` `m) ` `{ ` ` ` `// Using an adjacency list like representation ` ` ` `// to store numbers that lead to same ` ` ` `// remainder. ` ` ` `List<List<` `int` `>> v = ` `new` `List<List<` `int` `>>(m); ` ` ` `for` `(` `int` `i = 0; i < m; i++) ` ` ` `v.Add(` `new` `List<` `int` `>()); ` ` ` ` ` `for` `(` `int` `i = 0; i < n; i++) ` ` ` `{ ` ` ` ` ` `// stores the modulus when divided ` ` ` `// by m ` ` ` `int` `rem = a[i] % m; ` ` ` ` ` `v[rem].Add(a[i]); ` ` ` ` ` `// If we found k elements which ` ` ` `// have same remainder. ` ` ` `if` `(v[rem].Count == k) ` ` ` `{ ` ` ` `for` `(` `int` `j = 0; j < k; j++) ` ` ` `Console.Write(v[rem][j] + ` `" "` `); ` ` ` `return` `; ` ` ` `} ` ` ` `} ` ` ` ` ` `// If we could not find k elements ` ` ` `Console.Write(` `"-1"` `); ` `} ` ` ` `// Driver Code ` `public` `static` `void` `Main(String[] args) ` `{ ` ` ` `int` `[]a = { 1, 8, 4 }; ` ` ` `int` `n = a.Length; ` ` ` `print_result(a, n, 2, 3); ` `} ` `} ` ` ` `// This code is contributed by PrinciRaj1992 ` |

*chevron_right*

*filter_none*

## PHP

`<?php ` `// PHP program to find a list of k elements ` `// from an array such that difference between ` `// all of them is divisible by m. ` ` ` `// function to generate k numbers whose ` `// difference is divisible by m ` `function` `print_result(` `$a` `, ` `$n` `, ` `$k` `, ` `$m` `) ` `{ ` ` ` `// Using an adjacency list like representation ` ` ` `// to store numbers that lead to same ` ` ` `// remainder. ` ` ` `$v` `= ` `array_fill` `(0, ` `$m` `+ 1, ` `array` `()); ` ` ` ` ` `for` `(` `$i` `= 0; ` `$i` `< ` `$n` `; ` `$i` `++) ` ` ` `{ ` ` ` ` ` `// stores the modulus when divided ` ` ` `// by m ` ` ` `$rem` `= ` `$a` `[` `$i` `] % ` `$m` `; ` ` ` ` ` `array_push` `(` `$v` `[` `$rem` `], ` `$a` `[` `$i` `]); ` ` ` ` ` `// If we found k elements which ` ` ` `// have same remainder. ` ` ` `if` `(` `count` `(` `$v` `[` `$rem` `]) == ` `$k` `) ` ` ` `{ ` ` ` `for` `(` `$j` `= 0; ` `$j` `< ` `$k` `; ` `$j` `++) ` ` ` `echo` `$v` `[` `$rem` `][` `$j` `] . ` `" "` `; ` ` ` `return` `; ` ` ` `} ` ` ` `} ` ` ` ` ` `// If we could not find k elements ` ` ` `echo` `"-1"` `; ` `} ` ` ` `// Driver Code ` `$a` `= ` `array` `( 1, 8, 4 ); ` `$n` `= ` `count` `(` `$a` `); ` `print_result(` `$a` `, ` `$n` `, 2, 3); ` ` ` `// This code is contributed by mits ` `?> ` |

*chevron_right*

*filter_none*

**Output:**

1 4

**Time complexity:** O(n)

**Auxiliary Space:** O(m)

This article is contributed by **Raja Vikramaditya**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

## Recommended Posts:

- Number of pairs from the first N natural numbers whose sum is divisible by K
- Count pairs of numbers from 1 to N with Product divisible by their Sum
- Program to print all the numbers divisible by 3 and 5 for a given number
- Count the number of pairs (i, j) such that either arr[i] is divisible by arr[j] or arr[j] is divisible by arr[i]
- Count of pairs from 1 to a and 1 to b whose sum is divisible by N
- Count pairs (i,j) such that (i+j) is divisible by A and B both
- Largest divisible pairs subset
- Count pairs in array whose sum is divisible by K
- Count divisible pairs in an array
- Count pairs in array whose sum is divisible by 4
- Count number of pairs in array having sum divisible by K | SET 2
- Count numbers which are divisible by all the numbers from 2 to 10
- Print array elements that are divisible by at-least one other
- Print values of 'a' in equation (a+b) <= n and a+b is divisible by x
- Print all pairs in an unsorted array with equal sum