# Check if N and M can be made equal by increasing N by A and decreasing M by B

Given four numbers M, N, A and B, the task is to check whether M and N can be made equal to each other by doing any of the below operations:

• M can be increased by A and N can be decreased by B
• Leave both of them as it is.

Examples:

Input: M = 2, N = 8, A = 3, B = 3
Output: Yes
Explanation:
After first Operation:
M can be increased by A. Therefore, M = 2 + 3 = 5
N can be decreased by B. Therefore, N = 8 – 3 = 5
Finally, M = N = 5.

Input: M = 6, N = 4, A = 2, B = 1
Output: No

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

Approach: On careful observation, it can be observed that since we are increasing M and decreasing N, they can be made equal only when M is less than N. Therefore when M is less than N, there are two cases at each step:

1. M can be increased by A and N can be decreased by B.
2. Leave both of them as it is.

Another observation which can be made is that when M is increased and N is decreased, the absolute distance between M and N is reduced by the factor of A + B. For example:

Let M = 2, N = 14, A = 3 and B = 3.

• In step 1, M = 5 and N = 11. The absolute distance between M and N got reduced by 6. That is, initially, the absolute distance was 12(14 – 2). After performing the given step, the absolute distance became 6(11 – 5).
• In step 2, M = 8 and N = 8. The absolute distance between M and N again got reduced by 6 thereby making M and N equal.

From the above example, we can come to the conclusion that this problem can be solved in a constant time only by checking if the absolute distance between M and N is a multiple of (A + B) or not.

• If it is a multiple, then M and N can be made equal.
• Else, they cannot be made equal.

Below is the implementation of the above approach:

## C++

 `// C++ program to check if two numbers ` `// can be made equal by increasing ` `// the first by a and decreasing ` `// the second by b ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Function to whether the numbers ` `// can be made equal or not ` `bool` `checkEqualNo(``int` `m, ``int` `n, ``int` `a, ``int` `b) ` `{ ` `    ``if` `(m <= n) { ` ` `  `        ``// Check whether the numbers can reach ` `        ``// an equal point or not ` `        ``if` `((n - m) % (a + b) == 0) { ` `            ``return` `true``; ` `        ``} ` `        ``else` `{ ` `            ``return` `false``; ` `        ``} ` `    ``} ` `    ``else` `{ ` ` `  `        ``// M and N cannot be made equal by ` `        ``// increasing M and decreasing N when ` `        ``// M is already greater than N ` `        ``return` `false``; ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `M = 2, N = 8; ` `    ``int` `A = 3, B = 3; ` ` `  `    ``if` `(checkEqualNo(M, N, A, B))  ` `        ``cout << ``"Yes"` `<< endl; ` `    ``else` `        ``cout << ``"No"` `<< endl; ` ` `  `return` `0; ` `} `

## Java

 `// Java program to check if two numbers ` `// can be made equal by increasing ` `// the first by a and decreasing ` `// the second by b ` `class` `GFG  ` `{ ` `     `  `    ``// Function to whether the numbers ` `    ``// can be made equal or not ` `    ``static` `boolean` `checkEqualNo(``int` `m, ``int` `n, ``int` `a, ``int` `b) ` `    ``{ ` `        ``if` `(m <= n) { ` `     `  `            ``// Check whether the numbers can reach ` `            ``// an equal point or not ` `            ``if` `((n - m) % (a + b) == ``0``) { ` `                ``return` `true``; ` `            ``} ` `            ``else` `{ ` `                ``return` `false``; ` `            ``} ` `        ``} ` `        ``else` `{ ` `     `  `            ``// M and N cannot be made equal by ` `            ``// increasing M and decreasing N when ` `            ``// M is already greater than N ` `            ``return` `false``; ` `        ``} ` `    ``} ` `     `  `    ``// Driver code ` `    ``public` `static` `void` `main (String[] args) ` `    ``{ ` `        ``int` `M = ``2``, N = ``8``; ` `        ``int` `A = ``3``, B = ``3``; ` `     `  `        ``if` `(checkEqualNo(M, N, A, B) == ``true``)  ` `            ``System.out.println(``"Yes"``); ` `        ``else` `            ``System.out.println(``"No"``); ` `     `  `    ``} ` `} ` ` `  `// This code is contributed by Yash_R `

## Python3

 `# Python3 program to check if two numbers ` `# can be made equal by increasing ` `# the first by a and decreasing ` `# the second by b ` ` `  `# Function to whether the numbers ` `# can be made equal or not ` `def` `checkEqualNo(m, n, a, b) : ` `    ``if` `(m <``=` `n) : ` ` `  `        ``# Check whether the numbers can reach ` `        ``# an equal point or not ` `        ``if` `((n ``-` `m) ``%` `(a ``+` `b) ``=``=` `0``) : ` `            ``return` `True``; ` `     `  `        ``else` `: ` `            ``return` `False``; ` `         `  `    ``else` `: ` ` `  `        ``# M and N cannot be made equal by ` `        ``# increasing M and decreasing N when ` `        ``# M is already greater than N ` `        ``return` `False``; ` `     `  `# Driver code ` `if` `__name__ ``=``=` `"__main__"` `: ` ` `  `    ``M ``=` `2``; N ``=` `8``; ` `    ``A ``=` `3``; B ``=` `3``; ` ` `  `    ``if` `(checkEqualNo(M, N, A, B)) : ` `        ``print``(``"Yes"``); ` `    ``else` `: ` `        ``print``(``"No"``); ` ` `  `# This code is contributed by Yash_R `

## C#

 `// C# program to check if two numbers ` `// can be made equal by increasing ` `// the first by a and decreasing ` `// the second by b ` `using` `System; ` ` `  `class` `GFG  ` `{ ` `     `  `    ``// Function to whether the numbers ` `    ``// can be made equal or not ` `    ``static` `bool` `checkEqualNo(``int` `m, ``int` `n, ``int` `a, ``int` `b) ` `    ``{ ` `        ``if` `(m <= n) { ` `     `  `            ``// Check whether the numbers can reach ` `            ``// an equal point or not ` `            ``if` `((n - m) % (a + b) == 0) { ` `                ``return` `true``; ` `            ``} ` `            ``else` `{ ` `                ``return` `false``; ` `            ``} ` `        ``} ` `        ``else` `{ ` `     `  `            ``// M and N cannot be made equal by ` `            ``// increasing M and decreasing N when ` `            ``// M is already greater than N ` `            ``return` `false``; ` `        ``} ` `    ``} ` `     `  `    ``// Driver code ` `    ``public` `static` `void` `Main (String[] args) ` `    ``{ ` `        ``int` `M = 2; ` `        ``int` `N = 8; ` `        ``int` `A = 3; ` `        ``int` `B = 3; ` `     `  `        ``if` `(checkEqualNo(M, N, A, B) == ``true``)  ` `            ``Console.WriteLine(``"Yes"``); ` `        ``else` `            ``Console.WriteLine(``"No"``); ` `    ``} ` `} ` ` `  `// This code is contributed by Yash_R `

Output:

```Yes
```

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