A supply run must split n identical ration packs among k outposts arranged in a fixed order. Every outpost must receive at least one pack. Count the number of ways to assign the packs; two assignments differ if some outpost receives a different number of packs. If it is impossible (more outposts than packs), the answer is 0. Report the count modulo 1000000007.
Input format
A single line with two integers n and k.
Output format
A single integer: the number of valid assignments, modulo 1000000007.
Constraints
- 1 <= n <= 1000
- 1 <= k <= 1000