# Append X digits to the end of N to make it divisible by M

Given three positive integers **N**, **M**, and **X**, the task is to generate a number by appending **X** digits on the right side of **N** such that the number is divisible by **M**. If multiple solutions exist, then print any of them. Otherwise, print **-1**.

**Examples:**

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Input:N = 10, M = 5, X = 4Output:105555Explanation:One of possible values of N (= 10) by appending X(= 4) digits on the right side of N is 105555, which is divisible by M (= 5).

Input:N = 4, M = 50, X = 2Output:400

**Approach:** The idea is to append **X** digits on the right side of **N** by trying out all possible digits from the range **[0, 9]** and after appending **X** digits on the right side of N, check if the number is divisible by **M** or not. If found to be true, then print the number. Otherwise, print **-1**. Following are the recurrence relation:

Follow the steps below to solve the problem:

- Use the above recurrence relation, check if the number
**N**is divisible by**M**or not by appending**X**digits on the right side of**N**. If found to be true, then print the value of**N**by appending**X**digits. - Otherwise, print
**-1**.

Below is the implementation of the above approach :

## C++

`// C++ program to implement` `// the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to check if the value of N by` `// appending X digits on right side of N` `// is divisible by M or not` `bool` `isDiv(` `int` `N, ` `int` `X, ` `int` `M, ` `int` `& res)` `{` ` ` `// Base Case` ` ` `if` `(X == 0) {` ` ` `// If N is divisible` ` ` `// by M` ` ` `if` `(N % M == 0) {` ` ` `// Update res` ` ` `res = N;` ` ` `return` `true` `;` ` ` `}` ` ` `return` `false` `;` ` ` `}` ` ` `// Iterate over the range [0, 9]` ` ` `for` `(` `int` `i = 0; i <= 9; i++) {` ` ` `// If N is divisible by M by` ` ` `// appending X digits` ` ` `if` `(isDiv(N * 10 + i, X - 1, M, res)) {` ` ` `return` `true` `;` ` ` `}` ` ` `}` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `N = 4, M = 50, X = 2;` ` ` `// Stores the number by appending` ` ` `// X digits on the right side of N` ` ` `int` `res = -1;` ` ` `isDiv(N, X, M, res);` ` ` `cout << res;` `}` |

## Java

`// Java program for the above approach` `import` `java.io.*;` `import` `java.util.*;` `class` `GFG` `{` ` ` `// Function to check if the value of N by` ` ` `// appending X digits on right side of N` ` ` `// is divisible by M or not` ` ` `static` `int` `isDiv(` `int` `N, ` `int` `X, ` `int` `M, ` `int` `res)` ` ` `{` ` ` `// Base Case` ` ` `if` `(X == ` `0` `)` ` ` `{` ` ` `// If N is divisible` ` ` `// by M` ` ` `if` `(N % M == ` `0` `)` ` ` `{` ` ` `// Update res` ` ` `res = N;` ` ` `return` `res;` ` ` `}` ` ` `return` `res;` ` ` `}` ` ` `// Iterate over the range [0, 9]` ` ` `for` `(` `int` `i = ` `0` `; i < ` `9` `; i++)` ` ` `{` ` ` `// If N is divisible by M by` ` ` `// appending X digits` ` ` `int` `temp = isDiv(N * ` `10` `+ i, X - ` `1` `, M, res);` ` ` `if` `(temp != -` `1` `)` ` ` `{` ` ` `return` `temp;` ` ` `}` ` ` `}` ` ` `return` `res;` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `main(String[] args)` ` ` `throws` `java.lang.Exception` ` ` `{` ` ` `int` `N = ` `4` `, M = ` `50` `, X = ` `2` `;` ` ` `// Stores the number by appending` ` ` `// X digits on the right side of N` ` ` `int` `res = -` `1` `;` ` ` `res = isDiv(N, X, M, res);` ` ` `System.out.println(res);` ` ` `}` `}` `// This code is contributed by 18bhupenderyadav18.` |

## Python3

`# Python3 program to implement` `# the above approach` `# Function to check if the value of N by` `# appending X digits on right side of N` `# is divisible by M or not` `# global variable to store result` `res ` `=` `-` `1` `def` `isDiv(N, X, M):` ` ` `# Base case` ` ` `if` `(X ` `=` `=` `0` `):` ` ` `# If N is divisible` ` ` `# by M` ` ` `if` `(N ` `%` `M ` `=` `=` `0` `):` ` ` `global` `res` ` ` `res ` `=` `N` ` ` `return` `True` ` ` `return` `False` ` ` `# Iterate over the range [0, 9]` ` ` `for` `i ` `in` `range` `(` `10` `):` ` ` `# if N is Divisible by M upon appending X digits` ` ` `if` `(isDiv(N` `*` `10` `+` `i, X` `-` `1` `, M)):` ` ` `return` `True` `# Driver Code` `if` `__name__ ` `=` `=` `"__main__"` `:` ` ` `N, M, X ` `=` `4` `, ` `50` `, ` `2` ` ` `if` `(isDiv(N, X, M)):` ` ` `print` `(res)` ` ` `else` `:` ` ` `print` `(` `"-1"` `)` |

## C#

`// C# program to implement` `// the above approach ` `using` `System;` ` ` `class` `GFG` `{` ` ` ` ` `// Function to check if the value of N by` ` ` `// appending X digits on right side of N` ` ` `// is divisible by M or not` ` ` `static` `int` `isDiv(` `int` `N, ` `int` `X, ` `int` `M, ` `int` `res)` ` ` `{` ` ` ` ` `// Base Case` ` ` `if` `(X == 0)` ` ` `{` ` ` ` ` `// If N is divisible` ` ` `// by M` ` ` `if` `(N % M == 0)` ` ` `{` ` ` ` ` `// Update res` ` ` `res = N;` ` ` `return` `res;` ` ` `}` ` ` ` ` `return` `res;` ` ` `}` ` ` ` ` `// Iterate over the range [0, 9]` ` ` `for` `(` `int` `i = 0; i < 9; i++)` ` ` `{` ` ` ` ` `// If N is divisible by M by` ` ` `// appending X digits` ` ` `int` `temp = isDiv(N * 10 + i, X - 1, M, res);` ` ` `if` `(temp != -1)` ` ` `{` ` ` `return` `temp;` ` ` `}` ` ` `}` ` ` `return` `res;` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `N = 4, M = 50, X = 2;` ` ` ` ` `// Stores the number by appending` ` ` `// X digits on the right side of N` ` ` `int` `res = -1;` ` ` ` ` `res = isDiv(N, X, M, res);` ` ` `Console.WriteLine(res);` ` ` `}` `}` `// This code is contributed by sanjoy_62` |

## Javascript

`<script>` `// Javascript program to implement` `// the above approach` `var` `res = -1;` `// Function to check if the value of N by` `// appending X digits on right side of N` `// is divisible by M or not` `function` `isDiv(N, X, M)` `{` ` ` `// Base Case` ` ` `if` `(X == 0) {` ` ` `// If N is divisible` ` ` `// by M` ` ` `if` `(N % M == 0) {` ` ` `// Update res` ` ` `res = N;` ` ` `return` `true` `;` ` ` `}` ` ` `return` `false` `;` ` ` `}` ` ` `// Iterate over the range [0, 9]` ` ` `for` `(` `var` `i = 0; i <= 9; i++) {` ` ` `// If N is divisible by M by` ` ` `// appending X digits` ` ` `if` `(isDiv(N * 10 + i, X - 1, M)) {` ` ` `return` `true` `;` ` ` `}` ` ` `}` `}` `// Driver Code` `var` `N = 4, M = 50, X = 2;` `// Stores the number by appending` `// X digits on the right side of N` `isDiv(N, X, M, res);` `document.write(res);` `</script>` |

**Output**

400

**Time Complexity:** O(10^{X})**Auxiliary Space:** O(1)