Problem Description

A teacher has $N$ cookies and wants to distribute them to $k$ children.

Each child must receive at least one cookie, and the teacher wants every child to receive a different number of cookies. Determine whether the teacher can achieve this goal.

Input Format

This problem contains multiple groups of testdata within a single test point.

The input has a total of $T + 1$ lines.

The first line contains an integer $T$, representing the number of testdata groups.
The next $T$ lines each contain two integers $N, k$.

Output Format

Output $T$ lines, corresponding to the $T$ testdata groups in order.

• If it is possible, output Yes.
• If it is not possible, output No.

1
1 1

Yes

1
5 3

No

Hint

Constraints

• For $50\%$ of the testdata: $1 \le k \le 1000$, $1 \le N \le 10^6$.
• For $100\%$ of the testdata: $1 \le k, N \le 10^9$.
• $1 \le T \le 10^5$

Translated by ChatGPT 5