Description

Given the $n$ positive integers from $1$ to $n$, determine whether it is possible to choose exactly $k$ numbers such that the sum of the chosen numbers is $s$ (each number can be used at most once).

Input Format

This problem contains multiple test cases.

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

For each test case, one line contains three positive integers $n, k, s$.

Output Format

For each test case:

Output one line with a string, Yes or No, indicating whether it is possible to choose exactly $k$ numbers such that their sum is $s$.

3
5 2 10
5 2 5
5 2 2

No
Yes
No

Hint

This problem uses bundled testing.

• Subtask 1 (15 points): $n \le 5$.
• Subtask 2 (15 points): $n \le 15$.
• Subtask 3 (20 points): $n \le 100$.
• Subtask 4 (15 points): $k = 1$.
• Subtask 5 (15 points): $s \le 15$.
• Subtask 6 (20 points): no special constraints.

For $100\%$ of the testdata, $1 \le T \le 10^3$, $1 \le k \le n \le 10^9$, $1 \le s \le 10^{18}$.

Translated by ChatGPT 5