Problem: There is a grid with H horizontal rows and W vertical columns. Let (i, j) denote the square at the i-th row from the top and the j-th column from the left.

In the grid, N Squares (r_1, c_1), (r_2, c_2), \ldots, (r_N, c_N) are wall squares, and the others are all empty squares. It is guaranteed that Squares (1, 1) and (H, W) are empty squares.

Taro will start from Square (1, 1) and reach (H, W) by repeatedly moving right or down to an adjacent empty square.

Find the number of Taro's paths from Square (1, 1) to (H, W), modulo 10^9 + 7.

Constraints

* All values in input are integers.
* 2 \leq H, W \leq 10^5
* 1 \leq N \leq 3000
* 1 \leq r_i \leq H
* 1 \leq c_i \leq W
* Squares (r_i, c_i) are all distinct.
* Squares (1, 1) and (H, W) are empty squares.

Input

Input is given from Standard Input in the following format:


H W N
r_1 c_1
r_2 c_2
:
r_N c_N


Output

Print the number of Taro's paths from Square (1, 1) to (H, W), modulo 10^9 + 7.

Examples

Input

3 4 2
2 2
1 4


Output

3


Input

5 2 2
2 1
4 2


Output

0


Input

5 5 4
3 1
3 5
1 3
5 3


Output

24


Input

100000 100000 1
50000 50000


Output

123445622

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
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
 *
 * @author prakharjain
 */
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);
        YGrid2 solver = new YGrid2();
        solver.solve(1, in, out);
        out.close();
    }

    static class YGrid2 {
        int mod = 1000000007;
        int max = 200000;
        long[] fac = new long[max + 1];
        long[] ifac = new long[max + 1];

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int h = in.nextInt();
            int w = in.nextInt();

            int n = in.nextInt();

            cell[] cells = new cell[n];

            for (int i = 0; i < n; i++) {
                cells[i] = new cell(in.nextInt(), in.nextInt());
            }

            Arrays.sort(cells, (c1, c2) ->
            {
                if (c1.x <= c2.x && c1.y <= c2.y) {
                    return -1;
                } else if (c1.x >= c2.x && c1.y >= c2.y) {
                    return 1;
                } else {
                    return c1.x - c2.x;
                }
            });

            fac[0] = 1;
            ifac[0] = 1;

            for (int i = 1; i <= max; i++) {
                fac[i] = i * fac[i - 1];
                fac[i] %= mod;

                ifac[i] = pow(i, mod - 2, mod) * ifac[i - 1];
                ifac[i] %= mod;
            }

            long[] dp = new long[n];

            for (int i = 0; i < n; i++) {
                cell cc = cells[i];
                int x = cc.x;
                int y = cc.y;

                dp[i] = nCr(x + y - 2, x - 1, mod);

                for (int j = 0; j < i; j++) {
                    cell oc = cells[j];

                    int ox = oc.x;
                    int oy = oc.y;

                    if (ox <= x && oy <= y) {
                        long sub = dp[j];
                        sub *= nCr(x - ox + y - oy, x - ox, mod);
                        sub %= mod;

                        dp[i] -= sub;
                        dp[i] %= mod;
                    }
                }
            }

            long ans = nCr(h + w - 2, h - 1, mod);

            int x = h;
            int y = w;
            for (int j = 0; j < n; j++) {
                cell oc = cells[j];

                int ox = oc.x;
                int oy = oc.y;

                long sub = dp[j];
                sub *= nCr(x - ox + y - oy, x - ox, mod);
                sub %= mod;

                ans -= sub;
                ans %= mod;
            }

            if (ans < 0)
                ans += mod;

            out.println(ans);
        }

        long pow(long a, long p, int mod) {
            if (p == 0) {
                return 1;
            }

            long t = pow(a, p / 2, mod);

            if (p % 2 != 0) {
                return (((t * t) % mod) * a) % mod;
            } else {
                return (t * t) % mod;
            }
        }

        long nCr(int n, int r, int mod) {
            long ans = fac[n];
            ans *= ifac[n - r];
            ans %= mod;
            ans *= ifac[r];
            ans %= mod;

            return ans;
        }

        class cell {
            int x;
            int y;

            public cell(int x, int y) {
                this.x = x;
                this.y = y;
            }

        }

    }

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

        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 nextInt() {
            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 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 close() {
            writer.close();
        }

        public void println(long i) {
            writer.println(i);
        }

    }
}