Dice (I)

Medium Hard

LOJ-1145

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.

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).

Output

For each case print the case number and the result modulo 100000007 (10⁸ + 7).

Sample

Sample Input	Sample Output
Click to copy 5 1 6 3 2 9 8 500 6 1000 800 800 10000 2 100 10	Click to copy Case 1: 1 Case 2: 7 Case 3: 57286574 Case 4: 72413502 Case 5: 9

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#include <bits/stdc++.h>
using namespace std;
​
// Reads two integers and prints their sum
void basicIO() {
    int a, b;
    cin >> a >> b;
    cout << a + b << endl;
}
​
int main() {
    // basicIO();
    // Your cpp code here
    return 0;
}
​

Input

Output

Sample

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