Ideal Farm codeforces solution- 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.

Ideal Farm codeforces solution

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

The first line contains a single integer tt (1≤t≤1051≤t≤105) — the number of test cases.

The first and only line of each test case contains three integers ss, nn, and kk (1≤s,n,k≤10181≤s,n,k≤1018; n≤sn≤s).

 Ideal Farm solution codeforces

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

Example

input

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

 Ideal Farm solution codeforces

Copy
YES
NO
NO
YES
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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