A picker robot stands on the top-left cell of a warehouse grid that has H rows and W columns of cells. Each step it moves either one cell to the right (east) or one cell down (south). Count the number of distinct routes it can take to reach the bottom-right cell. Report the count modulo 1000000007.
Input format
A single line with two integers H and W.
Output format
A single integer: the number of monotone routes, modulo 1000000007.
Constraints
- 1 <= H <= 1000
- 1 <= W <= 1000