[Solution] Balls and Boxes CodeChef Solution

Problem

You have $N$ balls and $K$ boxes. You want to divide the $N$ balls into $K$ boxes such that:

• Each box contains $\ge 1$ balls.
• No two boxes contain the same number of balls.

Determine if it is possible to do so.

Input Format

• The first line contains a single integer $T$ — the number of test cases. Then the test cases follow.
• The first and only line of each test case contains two space-separated integers $N$ and $K$ — the number of balls and the number of boxes respectively.

Output Format

For each test case, output YES if it is possible to divide the $N$ balls into $K$ boxes such that the conditions are satisfied. Otherwise, output NO.

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You may print each character of YES and NO in uppercase or lowercase (for example, yes, yEs, Yes will be considered identical).

Explanation:

Test Case 1: It is not possible to divide the $3$ balls into $4$ boxes such that each box contains $\ge 1$ balls.

Test Case 2: One way to divide the $30$ balls into $3$ boxes is the following: $[5, 9, 16]$.

Test Case 3: It is not possible to divide the $2$ balls into $2$ boxes such that no two boxes contain the same number of balls.

Test Case 4: We can divide $1$ ball into $1$ box.