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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        DIrohaAndAGrid solver = new DIrohaAndAGrid();
        solver.solve(1, in, out);
        out.close();
    }

    static class DIrohaAndAGrid {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int h = in.readInt();
            int w = in.readInt();
            int a = in.readInt();
            int b = in.readInt();

            Modulo.mod = MiscUtils.MOD7;
            Modulo.buildCombination(200000);

            Modulo ans = new Modulo(0);
            for (int i = 1; i <= h - a; i++) {
                long left = Modulo.c(i + b - 2, i - 1);
                long right = Modulo.c(h - i + w - b - 1, h - i);
                ans.add(left * right);
            }
            out.printLine(ans);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void printLine(Object... objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }

    }

    static class Euclid {
        public static long[] extgcd(long a, long b, long[] is) {
            if (a == 0) {
                is[0] = 0;
                is[1] = 1;
                is[2] = b;
            } else {
                extgcd(b % a, a, is);
                long x = is[1] - b / a * is[0];
                is[1] = is[0];
                is[0] = x;
            }
            return is;
        }

    }

    static class Modulo {
        public static long mod;
        private long value;
        public static long[] nors;
        public static long[] revs;

        public Modulo(long value) {
            this.value = value;
        }

        public static long add(long a, long b) {
            return ((a + b) % mod + mod) % mod;
        }

        public static long mlt(long a, long b) {
            return (a * b) % mod;
        }

        public static long rev(long a) {
            return (Euclid.extgcd(a, mod, new long[3])[0] % mod + mod) % mod;
        }

        public Modulo add(long a) {
            setValue(add(value, a));
            return this;
        }

        public Modulo mlt(long a) {
            setValue(mlt(value, a));
            return this;
        }

        public static void buildCombination(int n) {
            nors = new long[n + 1];
            revs = new long[n + 1];

            nors[0] = 1;
            for (int i = 1; i <= n; i++) {
                nors[i] = mlt(nors[i - 1], i);
            }

            revs[n] = rev(nors[n]);
            for (int i = n - 1; i >= 0; i--) {
                revs[i] = mlt(revs[i + 1], i + 1);
            }
        }

        public static long c(int n, int k) {
            return n - k < 0 ? 0 : new Modulo(nors[n]).mlt(revs[k]).mlt(revs[n - k]).getValue();
        }

        public long getValue() {
            return value;
        }

        public void setValue(long value) {
            this.value = value;
        }

        public String toString() {
            return "" + value;
        }

    }

    static class MiscUtils {
        public static final int MOD7 = (int) (1e9 + 7);

    }
}