Problem Description
There is an old country and the king fell in love with a devil. The devil always ask the king to do some crazy things. Although the king used to be wise and beloved by his people. Now he is just like a boy in love and can’t refuse any request from the devil. Also, this devil is looking like a very cute Loli.
Something bad actually happen. The devil makes this kingdom's people infected by a disease called lolicon. Lolicon will take away people's life in silence.
Although z*p is died, his friend, y*wan is not a lolicon. Y*wan is the only one in the country who is immune of lolicon, because he like the adult one so much.
As this country is going to hell, y*wan want to save this country from lolicon, so he starts his journey.
You heard about it and want to help y*wan, but y*wan questioned your IQ, and give you a question, so you should solve it to prove your IQ is high enough.
The problem is about counting. How many undirected graphs satisfied the following constraints?
- This graph is a complete graph of size n.
- Every edge has integer cost from 1 to L.
- The cost of the shortest path from 1 to n is k.
Can you solve it?
output the answer modulo 10^9+7
Input
The first line contains an integer T, denoting the number of the test cases.
For each test case, the first line contains 3 integers n,k,L.
T<=5 n,k<=12,L<=10^9.
Output
For each test case, output the answer in one line.
Sample Input
2
3 3 3
4 4 4
Sample Output
8
668
