Assertion

Problem Description

Alice boldly asserts to you that if you divide $m$ items into $n$ groups, there will definitely be one group with a quantity of items greater than or equal to $d$. Due to Alice's excessive self-confidence, she is unaware that some of her assertions are actually incorrect. Your task is to determine whether Alice's assertion is correct. If Alice's assertion is true, output 'Yes'; otherwise, output 'No'.

Input

The input consists of multiple test cases. The first line contains a single integer $T(1\le T\le 10^5)$ — the number of test cases. Description of the test cases follows. The first line of each test case contains three integers $n,m,d$ $(2\le m\le10^9,1\le n \lt m,0\le d \le 10^9)$，$n$ and $m$ represent the number of groups and the quantity of items, respectively, in Alice's assertion. The symbol $d$ signifies Alice's claim that there will always be at least one group with a quantity of items greater than or equal to $d$.

Output

For each set of data, output a string. If Alice's assertion is correct, output 'Yes'; otherwise, output 'No'.

Sample Input

3
1 2 1
2 3 2
3 10 4

Sample Output

Yes
Yes
Yes

Source

2023“钉耙编程”中国大学生算法设计超级联赛（1）