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 $T$($1 ≤ T ≤ 10^5$) — the number of test cases. Description of the test cases follows.

The first line of each test case contains three integers $n$, $m$, $d$ ($2 ≤ m ≤ 10^9$, $1 ≤ n < m$, $0 ≤ d ≤ 10^9$), $n$ 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.

Example

3
1 2 1
2 3 2
3 10 4

Yes
Yes
Yes

Limitation

Time limit: 1 second

Memory limit: 256 megabytes