# Check if it is possible to make x and y zero at same time with given operation

Given two numbers X and Y. The task is to check whether X and Y can be reduced to zero at the same time by performing the following operation any number of times:

• Choose any natural number (say z) and reduce X and Y as one of the following at each operation:
1. X = X – z and Y = Y – 2*z
2. X = X – 2*z and Y = Y – z

Example:

Input: X = 6, Y = 9
Output: YES
Explanation:
We can perform operation in following way:
if z = 1, then
X = X – 2*z = 6 – 2*(1)
Y = Y – z = 9 – 1
=> X = 4 & Y = 8

Now again if z = 4, then
X = X – z = 4 – 4
Y = Y – 2*z = 8 – 2*(4)
=> X = 0 & Y = 0
Therefore, X & Y become zero in 2 steps assuming z as 1 and 4 respectively.

Input: X = 1, Y = 1
Output: NO
Explanation:
We don’t have any possible value for z such that X & Y can become zero simultaneously.

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

Approach:
Below are the observation for the given problem statement:

1. Since X and Y are updated to (X – z and Y – 2*z) or (X – 2*z and Y – z), therefore after n number of operations (X + Y) is updated to (X + Y – 3*n*z). Hence X and Y can be reduced to zero at simultaneously if (X+Y)%3 equals 0.
2. At each step one of the X or Y is reduced by 2*z. To reduced X and Y simultaneously zero it must satify this condition: max(X, Y)≤ 2*min(X, Y).
For Example:

Let X = 6 and Y = 15
Since (X+Y)%3 = (21%3) = 0
As our first condition is satisfied,
But by taking z = 6
X = X – z = 6 – 6 = 0
Y = Y – 2*z = 15 – 12 = 3
Since Y is not less than or equals to 2*X, therefore X and Y cannot be reduced to zero at same time.

If the above two conditions satisfy the values of X and Y, then X and Y can be reduced to 0 simultaneously.

Below is the implementation of the above approach:

## C++

 `// C++ program of the above approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to check if it is possible to ` `// make x and y can become 0 at same time ` `void` `canBeReduced(``int` `x, ``int` `y) ` `{ ` `    ``int` `maxi = max(x, y); ` `    ``int` `mini = min(x, y); ` ` `  `    ``// Check the given conditions ` `    ``if` `(((x + y) % 3) == 0 && maxi <= 2*mini) ` `        ``cout << ``"YES"` `<< endl; ` `    ``else` `        ``cout << ``"NO"` `<< endl; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `x = 6, y = 9; ` ` `  `    ``// Function Call ` `    ``canBeReduced(x, y); ` `    ``return` `0; ` `} `

## Java

 `// Java program of the above approach ` `import` `java.util.*; ` ` `  `class` `GFG{ ` `  `  `// Function to check if it is possible to ` `// make x and y can become 0 at same time ` `static` `void` `canBeReduced(``int` `x, ``int` `y) ` `{ ` `    ``int` `maxi = Math.max(x, y); ` `    ``int` `mini = Math.min(x, y); ` `  `  `    ``// Check the given conditions ` `    ``if` `(((x + y) % ``3``) == ``0` `&& maxi <= ``2``*mini) ` `        ``System.out.print(``"YES"` `+``"\n"``); ` `    ``else` `        ``System.out.print(``"NO"` `+``"\n"``); ` `} ` `  `  `// Driver Code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `x = ``6``, y = ``9``; ` `  `  `    ``// Function Call ` `    ``canBeReduced(x, y); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

## C#

 `// C# program of the above approach ` `using` `System;  ` ` `  `class` `GFG   ` `{  ` `    ``// Function to check if it is possible to ` `    ``// make x and y can become 0 at same time ` `    ``static` `void` `canBeReduced(``int` `x, ``int` `y) ` `    ``{ ` `        ``int` `maxi = Math.Max(x, y); ` `        ``int` `mini = Math.Min(x, y); ` `     `  `        ``// Check the given conditions ` `        ``if` `(((x + y) % 3) == 0 && maxi <= 2*mini) ` `            ``Console.WriteLine(``"YES"``); ` `        ``else` `            ``Console.WriteLine(``"NO"``);  ` `    ``} ` `     `  `    ``// Driver Code ` `    ``static` `void` `Main() ` `    ``{ ` `        ``int` `x = 6, y = 9; ` `     `  `        ``// Function Call ` `        ``canBeReduced(x, y); ` `    ``} ` `} ` ` `  `// This code is contributed by shubhamsingh10 `

## Python3

 `# Python 3 program of the above approach ` ` `  `# Function to check if it is possible to ` `# make x and y can become 0 at same time ` `def` `canBeReduced(x,y): ` `    ``maxi ``=` `max``(x, y) ` `    ``mini ``=` `min``(x, y) ` ` `  `    ``# Check the given conditions ` `    ``if` `(((x ``+` `y) ``%` `3``) ``=``=` `0` `and` `maxi <``=` `2``*``mini): ` `        ``print``(``"YES"``) ` `    ``else``: ` `        ``print``(``"NO"``) ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``x ``=` `6` `    ``y ``=` `9` ` `  `    ``# Function Call ` `    ``canBeReduced(x, y) ` `     `  `# This code is contributed by Surendra_Gangwar `

Output:

```YES
```

Time Complexity: O(1)

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