Ideal Farm solution Codeforces

Ideal Farm solution Codeforces

Theofanis decided to visit his uncle’s farm. There are 𝑠s animals and 𝑛n animal pens on the farm. For utility purpose, animal pens are constructed in one row.

Uncle told Theofanis that a farm is lucky if you can distribute all animals in all pens in such a way that there are no empty pens and there is at least one continuous segment of pens that has exactly 𝑘k animals in total.

Moreover, a farm is ideal if it’s lucky for any distribution without empty pens.

Neither Theofanis nor his uncle knows if their farm is ideal or not. Can you help them to figure it out?

Ideal Farm solution Codeforces

Input

The first line contains a single integer 𝑡t (1𝑡1051≤t≤105) — the number of test cases.

The first and only line of each test case contains three integers 𝑠s, 𝑛n, and 𝑘k (1𝑠,𝑛,𝑘10181≤s,n,k≤1018; 𝑛𝑠n≤s).

Output

For each test case, print YES (case-insensitive), if the farm is ideal, or NO (case-insensitive) otherwise.

Ideal Farm solution Codeforces

Example

input

Copy
4
1 1 1
1 1 2
100 50 200
56220 47258 14497

Ideal Farm solution Codeforces

output

Copy
YES
NO
NO
YES

Ideal Farm solution Codeforces

Note

For the first and the second test case, the only possible combination is [1][1] so there always will be a subsegment with 11 animal but not with 22 animals.

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