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: Runtime Error)

# -*- coding: utf-8 -*-
"""
Created on Fri Jul 26 05:23:03 2019

@author: matsui
"""

import numpy as np

def kai(a,b):
    ans=int(1)
    for i in range(a,b-1,-1):
        ans*=int(i)
    
    return int(ans)

def C(a,b):
    #x=np.arange(b+1,a+1)
    #y=np.arange(1,(a-b)+1)
    ans = kai(a,(b+1))/kai((a-b),1)
    return int(ans%(1e9+7))

H,W,A,B=map(int,input().split())

ans=0
for i in range(H-A):
    ans+=C((B-1+i),i)*C(((W-B-1)+(H-i-1)),(H-i-1))
    
       
ans=int(ans%(1e9+7))
print(ans)