One way of finding the maximum element in an array is to initialize a variable to the first element in the array, iterate through the remaining array, and update the variable whenever a value strictly greater than it is found. Assuming that the array contains N elements each in the range 1..K, how many such arrays exist such that the above algorithm performs exactly P updates? Initialization of the variable is not counted as an update.

For example, the possible arrays for N = 4, K = 3 and P = 2 are:

1. {1, 1, 2, 3}
2. {1, 2, 1, 3}
3. {1, 2, 2, 3}
4. {1, 2, 3, 1}
5. {1, 2, 3, 2}
6. {1, 2, 3, 3}

Input

The first line contains T the number of test cases. There follow T lines, containing 3 space separated integers N, K and P.

Output

Output T lines, one for each test case. On each line, output the answer as asked above. Since the answers can get very big, output the answer modulo 1000000007.

Example

Sample Input:
3
4 3 2
2 3 1
3 4 1

Sample Output:
6
3
30

Constraints

1 <= T <= 100
1 <= n <= 100
1 <= K <= 300
0 <= P < n