2018 Asia Singapore Preliminary Contest

Start

2018-09-14 18:00 AKDT

2018 Asia Singapore Preliminary Contest

End

2018-09-14 23:00 AKDT
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Problem I
Classical Counting

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

Two selections of size $K$ are considered different if the $K$-tuples for those selections are different. So, for example if $N=M=K=3$ (as in the second sample input), and the $N=3$ types of objects are labeled $A$, $B$, and $C$, then the tuple $(A,B,B)$ is different than $(B,A,B)$.

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