Problem:
Score : 400 points

Problem Statement

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.

Constraints

1 ≦ H, W ≦ 100,000

1 ≦ A < H

1 ≦ B < W

Input

The input is given from Standard Input in the following format:

H W A B

Output

Print the number of ways she can travel to the bottom-right cell, modulo 10^9+7.

Sample Input 1

2 3 1 1

Sample Output 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".

Sample Input 2

10 7 3 4

Sample Output 2

3570

There are 12 forbidden cells.

Sample Input 3

100000 100000 99999 99999

Sample Output 3

1

Sample Input 4

100000 100000 44444 55555

Sample Output 4

738162020

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

# -*- coding: utf-8 -*-
# スペース区切りの整数の入力
H, W, A, B = map(int, input().split())
T = [[-1 for i in range(W)] for j in range(H)]
S = 0 
# 初期値　2次元テーブルを作成
for i in range(W-1):
	T[0][i+1] = 1
for j in range(H-1):
	T[j+1][0] = 1
T[0][0]=0

# 下からA個,左からB個の枠に対して0による塗りつぶし
for j in range(A):
	for i in range(B):
		T[H-1-j][i] = 0

# 一つ左の升目と一つ上の升目を足し合わせて各升目に行く方法が何通りかを出力
for j in range(1,H):
	for i in range(1,W):
		if T[j][i] != 0:
			T[j][i] = T[j-1][i] + T[j][i-1]

print(T[H-1][W-1]%(10**9-7))