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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<iostream>
#define mod 1000000007
using namespace std;
typedef long long ll;

ll factorial[200005];
ll H, W, A, B;

void init() {
    factorial[0] = 1;
    for (ll i = 1; i <= H + W; i++) factorial[i] = i;
    for (ll i = 2; i <= H + W; i++) {
        factorial[i] = ((factorial[i] % mod) * (factorial[i - 1] % mod)) % mod;
    }
    return;
}

ll _pow(ll x, ll y) {
    ll ans = 1, z = x;
    while (y > 0) {
        if ((y & 1) == 1) {
            ans = ((ans % mod) * (z % mod)) % mod; 
        }
        z = ((z % mod) * (z % mod)) % mod;
        y /= 2;
    }
    return ans;
}

ll comb(ll x, ll y) {
    if (x == 0 || y == 0) return 1;
    ll div_num = ((factorial[x - y] % mod) * (factorial[y] % mod)) % mod;
    return (factorial[x] * (_pow(div_num, mod - 2) % mod)) % mod;
}

int main() {
    ll count = 0;
    cin >> H >> W >> A >> B;
    init();
    for (ll i = 1; i <= W - B; i++) {
        ll sub_count = comb(H - A + B + i - 2, H - A - 1);
        ll subsub_count = comb(A + W - B - i - 1, A - 1);
        count =  (count +  (((sub_count % mod) * (subsub_count % mod)) % mod)) % mod;
    }
    cout << count << endl;
    return 0;
}