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 PyPy3 (2.4.0) (judge verdict: Accepted)

import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools
from collections import deque

sys.setrecursionlimit(10**7)
inf = 10**20
mod = 10**9 + 7

DR = [1, -1, 0, 0]
DC = [0, 0, 1, -1]

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
     

fac = [-1] * (2 * 10**6+1)
inv = [-1] * (2 * 10**6+1)
finv = [-1] * (2 * 10**6+1)

fac[0] = fac[1] = 1
inv[1] = 1
finv[0] = finv[1] = 1

def initNCMMod(limit):
    for i in range(2, limit):
        fac[i] = fac[i-1] * i % mod
        inv[i] = mod - inv[mod%i] * (mod // i) % mod
        finv[i] = finv[i-1] * inv[i] % mod

def NCMMod(n, k):
    if n < k:
        return 0
    if (n < 0 or k < 0):
        return 0
    return fac[n] * (finv[k] * finv[n-k] % mod) % mod

initNCMMod(2 * 10**6 + 1)
def main():
    H, W, A, B = LI()
    cnt = 0
    for i in range(H-A):
        way = NCMMod(B + i - 1, i) * NCMMod(W + H - B - i - 2, W - 1 - B)
        way %= mod
        cnt += way
        cnt %= mod
    print(cnt)


main()