# Check if X and Y can be made zero by using given operation any number of times

Given two integers X and Y, the task is to check if these two integers can be made equal to 0 by using the given operation any number of times. An operation is described as follows –

• Choose an arbitrary integer Z.
• Update the values with either of the following values:
• X = X – 2*Z and Y = Y – 3*Z
• X = X – 3*Z and Y = Y – 2*Z

Examples:

Input: X = 6, Y = 9
Output: Yes
Explanation:
Operation 1: Choose Z = 3, X = 6 – 2*3 = 0 and Y = 9 – 3*3 = 0
Since X and Y can be made equal to 0 using 1 operation, the required answer is Yes.

Input: X = 33, Y = 27
Output: Yes
Explanation:
Operation 1: Choose Z = 9, X := 33 – 3*9 = 6 and Y := 27 – 2*9 = 9
Operation 2: Choose Z = 3, X := 6 – 2*3 = 0 and Y := 9 – 3*3 = 0
Since X and Y can be made equal to 0 using 2 operation, the required answer is Yes.

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: Let’s assume X ≤ Y. Then the answer is Yes if two following conditions holds:

• (X + Y) mod 5 = 0: because after each operation the value (X + Y) mod 5 does not change.
Let’s assume some arbitrary number Z has been chosen.
Therefore, the value (X + Y) will be changed to

`((X - 3Z) + (Y - 2Z))`

This is equal to

`(X + Y - 5Z)`

For this value to be equal to 0, X + Y = 5Z. Therefore, on taking mod on both the sides, (X + Y) mod 5 has to be equal to 0.

• 3*X >= 2*Y so that the subtraction doesnt make the values of X and Y negative.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Function to check if X and Y ` `// can be made equal to zero by ` `// using given operation any number of times ` `void` `ifPossible(``int` `X, ``int` `Y) ` `{ ` `    ``if` `(X > Y) ` `        ``swap(X, Y); ` ` `  `    ``// Check for the two conditions ` `    ``if` `((X + Y) % 5 == 0 and 3 * X >= 2 * Y) ` `        ``cout << ``"Yes"``; ` `    ``else` `        ``cout << ``"No"``; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `X = 33, Y = 27; ` ` `  `    ``ifPossible(X, Y); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `class` `GFG ` `{ ` ` `  `// Function to check if X and Y ` `// can be made equal to zero by ` `// using given operation any number of times ` `static` `void` `ifPossible(``int` `X, ``int` `Y) ` `{ ` `    ``if` `(X > Y) ` `        ``swap(X, Y); ` ` `  `    ``// Check for the two conditions ` `    ``if` `((X + Y) % ``5` `== ``0` `&& ``3` `* X >= ``2` `* Y) ` `        ``System.out.print(``"Yes"``); ` `    ``else` `        ``System.out.print(``"No"``); ` `} ` `static` `void` `swap(``int` `x, ``int` `y) ` `{ ` `    ``int` `temp = x; ` `    ``x = y; ` `    ``y = temp; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `X = ``33``, Y = ``27``; ` ` `  `    ``ifPossible(X, Y); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

## Python3

 `# Python3 implementation of the approach ` ` `  `# Function to check if X and Y ` `# can be made equal to zero by ` `# using given operation any number of times ` `def` `ifPossible(X, Y): ` `    ``if` `(X > Y): ` `        ``X, Y ``=` `Y, X ` ` `  `    ``# Check for the two conditions ` `    ``if` `((X ``+` `Y) ``%` `5` `=``=` `0` `and` `3` `*` `X >``=` `2` `*` `Y): ` `        ``print``(``"Yes"``) ` `    ``else``: ` `        ``print``(``"No"``) ` ` `  `# Driver code ` `X ``=` `33` `Y ``=` `27` ` `  `ifPossible(X, Y) ` ` `  `# This code is contributed by mohit kumar 29 `

## C#

 `// C# implementation of the approach ` `using` `System; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to check if X and Y ` `// can be made equal to zero by ` `// using given operation any number of times ` `static` `void` `ifPossible(``int` `X, ``int` `Y) ` `{ ` `    ``if` `(X > Y) ` `        ``swap(X, Y); ` ` `  `    ``// Check for the two conditions ` `    ``if` `((X + Y) % 5 == 0 && 3 * X >= 2 * Y) ` `        ``Console.WriteLine(``"Yes"``); ` `    ``else` `        ``Console.WriteLine(``"No"``); ` `} ` `static` `void` `swap(``int` `x, ``int` `y) ` `{ ` `    ``int` `temp = x; ` `    ``x = y; ` `    ``y = temp; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main() ` `{ ` `    ``int` `X = 33, Y = 27; ` ` `  `    ``ifPossible(X, Y); ` `} ` `} ` ` `  `// This code is contributed by Yash_R `

Output:

```Yes
```

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