Score : 400 points
We have a large square grid with H rows and W columns. Iroha is now standing in the top-left cell. She will repeat going right or down to the adjacent cell, until she reaches the bottom-right cell.
However, she cannot enter the cells in the intersection of the bottom A rows and the leftmost B columns. (That is, there are A×B forbidden cells.) There is no restriction on entering the other cells.
Find the number of ways she can travel to the bottom-right cell.
Since this number can be extremely large, print the number modulo 10^9+7.
The input is given from Standard Input in the following format:
H W A B
Print the number of ways she can travel to the bottom-right cell, modulo 10^9+7.
2 3 1 1
2
We have a 2×3 grid, but entering the bottom-left cell is forbidden. The number of ways to travel is two: "Right, Right, Down" and "Right, Down, Right".
10 7 3 4
3570
There are 12 forbidden cells.
100000 100000 99999 99999
1
100000 100000 44444 55555
738162020