# 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:- X = X – z and Y = Y – 2*z
- 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.

**Approach:**

Below are the observation for the given problem statement:

- 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**. - 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 <bits/stdc++.h> ` `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; ` `} ` |

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## 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 ` |

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## 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 ` |

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## 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 ` |

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**Output:**

YES

**Time Complexity:** O(1)

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