New Restaurant

Problem code: NEWREST

All submissions for this problem are available.

Chef Dengklek will open a new restaurant in the city. The restaurant will be open for N days. He can cook M different types of dish. He would like to cook a single dish every day, such that for the entire N days, he only cook at most K distinct types of dishes.

In how many ways can he do that?

Input

The first line contains a single integer T, the number of test cases. T test cases follow. Each test case consists of a single line consisting of three integers N, M, K.

Output

For each test case, output a single line consisting the number of different ways he can cook for the entire N days, modulo 1000000007.

Constraints

1 ≤ T ≤ 100
1 ≤ N ≤ 1000
1 ≤ M ≤ 1000000
1 ≤ K ≤ 1000

Example

Input:

Output:

Date:	2011-09-06
Time limit:	2s
Source limit:	50000B
Languages:	All

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Program should read from standard input and write to standard output.

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