# PROBLEM LINK:

Practice

Contest: Division 1

Contest: Division 2

Contest: Division 3

Contest: Division 4

* Author:* Utkarsh Gupta

*Nishank Suresh, Takuki Kurokawa*

**Testers:***Nishank Suresh*

**Editorialist:**# DIFFICULTY:

1163

# PREREQUISITES:

None

# PROBLEM:

Given two integers A and B, is it possible to add a non-negative integer K to both of them such that A+K is a divisor of B+K?

# EXPLANATION:

First, if A = B, then the answer is obviously “Yes”.

Otherwise, note that no matter which K we choose, the difference between A and B remains constant.

Let d = B - A. A valid K exists if and only if A \leq d.

## Proof

If A \leq d, then choose K = d - A.

This makes A = d and B = 2d, and of course A is now a factor of B.

Conversely, suppose A \gt d. Suppose, for some K, A+K is a factor of B+K. Then, there exists an x \geq 1 such that:

But A \gt d, so A+K \gt d. This means a valid only exists in the case when d = 0, when we can choose x = 1.

However, we assumed A \neq B, which implies d \neq 0, so this case cannot happen.

This completes the proof.

# TIME COMPLEXITY

\mathcal{O}(1) per test case.

# CODE:

## Editorialist's code (Python)

```
for _ in range(int(input())):
a, b = map(int, input().split())
d = b - a
print('Yes' if d == 0 or a <= d else 'No')
```