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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.UncheckedIOException;
import java.util.StringTokenizer;

class Main{
	static int max=200000;	//nCr の n の最大値?
	static long MOD=1000000007;
	static long[] fac=new long[max];
	static long[] finv=new long[max];
	static long[] inv=new long[max];
	public static void main(String[] args){
		COMinit();		//下ごしらえ
		SC sc=new SC(System.in);
		long sum=0;
		int H=sc.nextInt();
		int W=sc.nextInt();
		int A=sc.nextInt();
		int B=sc.nextInt();
		long[] wake=new long[H-A];
		for(int i=0; i<H-A; i++) {
			wake[i]=COM(B-1+i,i);
		}
		for(int i=0; i<H-A; i++) {
			wake[i]*=COM(W-B+H-2-i,H-1-i);
			wake[i]%=MOD;
		}
		for(int i=0; i<H-A; i++) {
			sum+=wake[i];
			sum%=MOD;
		}
		pl(sum);
	}
	public static void pl(Object o) {
		System.out.println(o);
	}
	public static void pl() {
		System.out.println();
	}
	public static void p(Object o) {
		System.out.print(o);
	}
	static class SC {
		private BufferedReader reader = null;
		private StringTokenizer tokenizer = null;
		public SC(InputStream in) {
			reader = new BufferedReader(new InputStreamReader(in));
		}
		public String next() {
			if (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new UncheckedIOException(e);
				}
			}
			return tokenizer.nextToken();
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
		public double nextDouble() {
			return Double.parseDouble(next());
		}
		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new UncheckedIOException(e);
			}
		}
	}
	static void COMinit() {		//テーブルを作るみたい nCrの　または　階乗の？
		fac[0] = fac[1] = 1;
		finv[0] = finv[1] = 1;
		inv[1] = 1;
		for (int i = 2; i < max; i++){
			fac[i] = fac[i - 1] * i % MOD;
			inv[i] = MOD - inv[(int)(MOD%i)] * (MOD / i) % MOD;
			finv[i] = finv[i - 1] * inv[i] % MOD;
		}
	}
	static long COM(int n, int k){			//二項係数の計算
		if (n < k) return 0;
		if (n < 0 || k < 0) return 0;
		return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
	}
}