Background

Click here (or at the bottom of this page) to download the English version of statements for this contest (PDF).

Problem Description

She has a wooden stick of length $m$.

She wants you to cut this stick into $n$ smaller sticks, such that each smaller stick has a positive integer length, and any $3$ of the smaller sticks you choose can form a triangle by connecting end to end.

You want to determine whether you can satisfy her wish.

Input Format

This problem contains multiple test cases.

The first line contains a positive integer $T$, which denotes the number of test cases.

Then follow the test cases. For each test case, there is one line containing two integers $n, m$.

Output Format

For each test case, output one string per line:

• If you can satisfy her wish, output Yes.
• If you cannot, output No.

3
4 7
3 4
5 21

Yes
No
Yes

Hint

"Sample Explanation #1"

For the $1$-st test case, you can cut the stick into smaller sticks with lengths $1, 2, 2, 2$.

For the $2$-nd test case, it can be proven that there is no solution that meets the requirements.

For the $3$-rd test case, one feasible solution is to cut the stick into smaller sticks with lengths $3, 4, 4, 5, 5$.

"Constraints"

For all testdata, it is guaranteed that:

• $1 \le T \le 100$.
• $3 \le n \le m \le 10^9$.

This problem uses bundled tests.

• Subtask 0 (18 points): $m \le 500$, $n = 3$.
• Subtask 1 (15 points): $n = 3$.
• Subtask 2 (32 points): $n \times 2 \ge m$.
• Subtask 3 (35 points): No special constraints.

Translated by ChatGPT 5