Classical Counting

You have $N$ objects, each with $M$ copies. How many ways are there to take exactly $K$ of them?

Input

The first line of input contains three integers, $N$, $M$ and $K$ respectively, subjected to $1 \leq N, M, K \leq 10^5$.

Output

Output the number of ways. As the number of ways could be large, output them modulo $10^6 + 7$.

Sample Input 1 Sample Output 1
10 1 2
45
Sample Input 2 Sample Output 2
3 3 3
10
Sample Input 3 Sample Output 3
3 2 7
0