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: Time Limit Exceeded)

import math
from collections import deque
# H,W,A,B=map(int,input().split())
# H,W,A,B=10,7,3,4
H,W,A,B=100000,100000,44444,55555
# array=[[0 for i in range(W)] for j in range(H)]

#S->P->G の実装
#与えられたHとWで最大値を算出
# ue=math.factorial( H-1 + W-1 )
# sita=math.factorial( H-1 )*math.factorial( W-1 )
# result = ue//sita
# print(result)
# print("---------------")
ans=[]
mod = 10**9+7
#S->PとP->Gの実装
for i in range(0,H-A):
    ue=math.factorial( H-i-1 + W-B-1 )
    sita=math.factorial( H-i-1 )*math.factorial( W-B-1 )
    result1 = ue//sita

    ue=math.factorial( i + B-1)
    sita=math.factorial(i)*math.factorial(B-1)
    result2 = ue // sita
    # print("S->P",result1)
    # print("P->G",result2)
    # print("S->P->G",result1*result2)
    ans.append(result1*result2)

# ue=math.factorial( H-A-1 + W-B-1 )
# sita=math.factorial( H-A-1 )*math.factorial( W-B-1 )
# result = ue//sita
# print("S->P",result)

# ue=math.factorial( A + B-1)
# sita=math.factorial(A)*math.factorial(B-1)
# result = ue // sita
# print("P->G",result)

print(sum(ans)//mod)
# print(*array,sep="\n")
# print(array[H-1][W-1])