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: Wrong Answer)


mod = 10**9+7


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


class Fact():
    def __init__(self, H, W):
        self.mod = 10**9+7
        self.facts = [1]*(H+W-1)
        for i in range(1, H+W-1):
            self.facts[i] = self.facts[i-1]*i % mod

        self.i = [pow(self.facts[-1], mod-2, mod)]
        for i in range(1, H+W-1)[::-1]:
            self.i.append(self.i[-1]*i % mod)
        self.i.reverse()

    def comb(self, n, r):
        ret = self.facts[n] * self.i[n-r]*self.i[r]
        return ret

    def print_fact(self):
        print(self.facts)


f = Fact(H, W)

all_path = f.comb(H+W-2, H-1)

f.print_fact()

remove_path = 0
for i in range(B):
    tmp = f.comb(H-A+i-1, i)
    tmp *= f.comb(W-i-1+A-1, A-1)
    remove_path += tmp

remove_path %= mod

print((all_path - remove_path) % mod)