# Check if a number S can be made divisible by D by repeatedly adding the remainder to S

Given two integers **S** and **D**, the task is to check if the integer **S** can be made divisible by **D** or not by repeatedly adding **S** modulo **D** to **S**. If **S** is divisible by **D**, then print **“Yes”**. Otherwise, print **“No”**.

**Examples:**

Input:S = 3, D = 6Output:YesExplanation:

Lets say that the value on the i^{th}interval mod D is V(i) i.e.,V(i) = (V(i – 1) + V(i – 1) % D) % Dthen,

V(0) = S % D = 3

V(1) = (V(0) + V(0) % D) % D = (3 + (3%6)) % 6 = 0

So, 6 is divisible by 6. Therefore, print “Yes”.

Input:S = 1, D = 5Output:No

**Approach:** The given problem can be solved by using Pigeon Hole Principle. Follow the below steps to solve the problem:

- According to the principle, if there are more than
**D**numbers that are taken modulo with**D**, then at least one value in the range**([0, D – 1])**will occur twice. - Iterate for
**(D + 1)**times and store the value of**V(i)**in a HashMap, and if there is a repetition then break out of the loop. - There is an edge case when the remainder value is
**0**, exit out of the loop in that case as well as this is a case of divisibility, but our logic treats it as a cycle.

Below is the implementation of the above approach:

## C++

`// C++ program for the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to check if S is divisible` `// by D while changing S to (S + S%D)` `string isDivisibleByDivisor(` `int` `S, ` `int` `D)` `{` ` ` `// V(0) = S % D` ` ` `S %= D;` ` ` `// Stores the encountered values` ` ` `unordered_set<` `int` `> hashMap;` ` ` `hashMap.insert(S);` ` ` `for` `(` `int` `i = 0; i <= D; i++) {` ` ` `// V(i) = (V(i-1) + V(i-1)%D) % D` ` ` `S += (S % D);` ` ` `S %= D;` ` ` `// Check if the value has` ` ` `// already been encountered` ` ` `if` `(hashMap.find(S)` ` ` `!= hashMap.end()) {` ` ` `// Edge Case` ` ` `if` `(S == 0) {` ` ` `return` `"Yes"` `;` ` ` `}` ` ` `return` `"No"` `;` ` ` `}` ` ` `// Otherwise, insert it into` ` ` `// the hashmap` ` ` `else` ` ` `hashMap.insert(S);` ` ` `}` ` ` `return` `"Yes"` `;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `S = 3, D = 6;` ` ` `cout << isDivisibleByDivisor(S, D);` ` ` `return` `0;` `}` |

## Java

`// Java program for the above approach` `import` `java.lang.*;` `import` `java.util.*;` `class` `GFG{` ` ` `// Function to check if S is divisible` `// by D while changing S to (S + S%D)` `static` `String isDivisibleByDivisor(` `int` `S, ` `int` `D)` `{` ` ` ` ` `// V(0) = S % D` ` ` `S %= D;` ` ` `// Stores the encountered values` ` ` `Set<Integer> hashMap = ` `new` `HashSet<>();` ` ` `hashMap.add(S);` ` ` `for` `(` `int` `i = ` `0` `; i <= D; i++)` ` ` `{` ` ` ` ` `// V(i) = (V(i-1) + V(i-1)%D) % D` ` ` `S += (S % D);` ` ` `S %= D;` ` ` `// Check if the value has` ` ` `// already been encountered` ` ` `if` `(hashMap.contains(S))` ` ` `{` ` ` ` ` `// Edge Case` ` ` `if` `(S == ` `0` `)` ` ` `{` ` ` `return` `"Yes"` `;` ` ` `}` ` ` `return` `"No"` `;` ` ` `}` ` ` `// Otherwise, insert it into` ` ` `// the hashmap` ` ` `else` ` ` `hashMap.add(S);` ` ` `}` ` ` `return` `"Yes"` `;` `}` `// Driver code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `S = ` `3` `, D = ` `6` `;` ` ` ` ` `System.out.println(isDivisibleByDivisor(S, D));` `}` `}` `// This code is contributed by offbeat` |

## Python3

`# Python 3 program for the above approach` `# Function to check if S is divisible` `# by D while changing S to (S + S%D)` `def` `isDivisibleByDivisor(S, D):` ` ` `# V(0) = S % D` ` ` `S ` `%` `=` `D` ` ` `# Stores the encountered values` ` ` `hashMap ` `=` `set` `()` ` ` `hashMap.add(S)` ` ` `for` `i ` `in` `range` `(D` `+` `1` `):` ` ` ` ` `# V(i) = (V(i-1) + V(i-1)%D) % D` ` ` `S ` `+` `=` `(S ` `%` `D)` ` ` `S ` `%` `=` `D` ` ` `# Check if the value has` ` ` `# already been encountered` ` ` `if` `(S ` `in` `hashMap):` ` ` ` ` `# Edge Case` ` ` `if` `(S ` `=` `=` `0` `):` ` ` `return` `"Yes"` ` ` `return` `"No"` ` ` `# Otherwise, insert it into` ` ` `# the hashmap` ` ` `else` `:` ` ` `hashMap.add(S)` ` ` `return` `"Yes"` `# Driver Code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` `S ` `=` `3` ` ` `D ` `=` `6` ` ` `print` `(isDivisibleByDivisor(S, D))` ` ` `# This code is contributed by bgangwar59.` |

## C#

`// C# program for the above approach` `using` `System;` `using` `System.Linq;` `using` `System.Collections.Generic;` `class` `GFG {` ` ` `// Function to check if S is divisible` `// by D while changing S to (S + S%D)` `static` `string` `isDivisibleByDivisor(` `int` `S, ` `int` `D)` `{` ` ` `// V(0) = S % D` ` ` `S %= D;` ` ` ` ` `// Stores the encountered values` ` ` `List<` `int` `> hashMap = ` `new` `List<` `int` `>();;` ` ` `hashMap.Add(S);` ` ` ` ` `for` `(` `int` `i = 0; i <= D; i++) {` ` ` ` ` `// V(i) = (V(i-1) + V(i-1)%D) % D` ` ` `S += (S % D);` ` ` `S %= D;` ` ` ` ` `// Check if the value has` ` ` `// already been encountered` ` ` `if` `(hashMap.Contains(S)) {` ` ` ` ` `// Edge Case` ` ` `if` `(S == 0) {` ` ` `return` `"Yes"` `;` ` ` `}` ` ` `return` `"No"` `;` ` ` `}` ` ` ` ` `// Otherwise, insert it into` ` ` `// the hashmap` ` ` `else` ` ` `hashMap.Add(S);` ` ` `}` ` ` `return` `"Yes"` `;` `}` ` ` `// Driver Code` ` ` `static` `void` `Main()` ` ` `{` ` ` `int` `S = 3, D = 6;` ` ` `Console.Write( isDivisibleByDivisor(S, D));` ` ` `}` `}` `// This code is contributed by sanjoy_62.` |

## Javascript

`<script>` ` ` `// JavaScript program for the above approach` ` ` `// Function to check if S is divisible` ` ` `// by D while changing S to (S + S%D)` ` ` `function` `isDivisibleByDivisor(S, D)` ` ` `{` ` ` ` ` `// V(0) = S % D` ` ` `S %= D;` ` ` `// Stores the encountered values` ` ` `var` `hashMap = [];` ` ` `hashMap.push(S);` ` ` `for` `(` `var` `i = 0; i <= D; i++)` ` ` `{` ` ` ` ` `// V(i) = (V(i-1) + V(i-1)%D) % D` ` ` `S += S % D;` ` ` `S %= D;` ` ` `// Check if the value has` ` ` `// already been encountered` ` ` `if` `(hashMap.includes(S)) {` ` ` `// Edge Case` ` ` `if` `(S == 0) {` ` ` `return` `"Yes"` `;` ` ` `}` ` ` `return` `"No"` `;` ` ` `}` ` ` `// Otherwise, insert it into` ` ` `// the hashmap` ` ` `else` `hashMap.push(S);` ` ` `}` ` ` `return` `"Yes"` `;` ` ` `}` ` ` `// Driver Code` ` ` `var` `S = 3,` ` ` `D = 6;` ` ` `document.write(isDivisibleByDivisor(S, D));` ` ` ` ` `// This code is contributed by rdtank.` ` ` `</script>` |

**Output:**

Yes

**Time Complexity:** O(D)**Auxiliary Space:** O(D)