8985: LightOJ - Dice (I)
[Creator : ]
Description
You have $N$ dices; each of them has $K$ faces numbered from $1$ to $K$.
Now you have arranged the $N$ dices in a line. You can rotate/flip any dice if you want.
How many ways you can set the top faces such that the summation of all the top faces equals $S$?
Now you are given $N, K, S$; you have to calculate the total number of ways.
Now you have arranged the $N$ dices in a line. You can rotate/flip any dice if you want.
How many ways you can set the top faces such that the summation of all the top faces equals $S$?
Now you are given $N, K, S$; you have to calculate the total number of ways.
Input
Input starts with an integer $T (≤ 25)$, denoting the number of test cases.
Each case contains three integers: $N\ (1 ≤ N ≤ 1000),\ K\ (1 ≤ K ≤ 1000)$ and $S\ (0 ≤ S ≤ 15000)$.
Each case contains three integers: $N\ (1 ≤ N ≤ 1000),\ K\ (1 ≤ K ≤ 1000)$ and $S\ (0 ≤ S ≤ 15000)$.
Output
For each case print the case number and the result modulo $100000007\ (10^8 + 7)$.
Sample 1 Input
5
1 6 3
2 9 8
500 6 1000
800 800 10000
2 100 10
Sample 1 Output
Case 1: 1
Case 2: 7
Case 3: 57286574
Case 4: 72413502
Case 5: 9