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 ≤ T ≤ 105) — 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 ≤ m ≤ 109, 1 ≤ n < m, 0 ≤ d ≤ 109) , 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.

ouput

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

Example

Input：

3
1 2 1
2 3 2
3 10 4

ouput：

Yes
Yes
Yes