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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

public class Main {
	static final long MOD=1000000007;//998244353;
	public static void main(String[] args) {
		PrintWriter out = new PrintWriter(System.out);
		InputReader sc=new InputReader(System.in);
		int H=sc.nextInt();
		int W=sc.nextInt();
		int N=sc.nextInt();
		ArrayList<Pair> arrayList=new ArrayList<>();
		for (int i = 0; i < N; i++) {
			int r=sc.nextInt()-1;
			int c=sc.nextInt()-1;
			arrayList.add(new Pair(r, c));
		}
		Binomial binomial=new Binomial();
		arrayList.add(new Pair(H-1, W-1));
		Collections.sort(arrayList);
		long[] dp=new long[N+1];
		for (int i = 0; i <= N; i++) {
			int r=arrayList.get(i).x;
			int c=arrayList.get(i).y;
			dp[i]=binomial.nCk(r+c, r, MOD);
			for (int j = 0; j < i; j++) {
				int r_=arrayList.get(j).x;
				int c_=arrayList.get(j).y;
				if (r-r_<0||c-c_<0) {
					continue;
				}
				dp[i]-=(dp[j]*binomial.nCk(r-r_+c-c_, c-c_, MOD))%MOD;
				if (dp[i]<0) {
					dp[i]+=MOD;
				}
			}
		}
		System.out.println(dp[N]);
   	}
	static class Pair implements Comparable<Pair>{
    	public int x;
    	public int y;
    	public Pair(int x,int y) {
    		this.x=x;
    		this.y=y;
    	}
    	@Override
    	public boolean equals(Object obj) {
    		if(obj instanceof Pair) {
    			Pair other = (Pair) obj;
    			return other.x==this.x && other.y==this.y;
    		}
    		return false;
    	}//同値の定義
    	@Override
    	public int hashCode() {
    		return Objects.hash(this.x,this.y);
    	}//これ書かないと正しく動作しない（要　勉強）
    	@Override
    	public int compareTo( Pair p){
    		if (this.x+this.y>p.x+p.y) {
    			return 1;
    		}
    		else if (this.x+this.y<p.x+p.y) {
    			return -1;
    		}
    		else {
    			return 0;
    		}
    	}
    }
	static class Binomial{
		int MAX = 510000;//ほしいサイズ
		long[] fac=new long[MAX];
		long[] finv=new long[MAX];
		long[] inv=new long[MAX];
		public Binomial(){
			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;
		    }//facがx!、finvがx!の逆元,10^7くらいまでのテーブル(MAXまで)
		}
		long nCk(int n,int k,long MOD) {
		    if (n < k) return 0;
		    if (n < 0 || k < 0) return 0;
		    return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
		}
	}
		static class InputReader { 
		private InputStream in;
		private byte[] buffer = new byte[1024];
		private int curbuf;
		private int lenbuf;
		public InputReader(InputStream in) {
			this.in = in;
			this.curbuf = this.lenbuf = 0;
		}
 
		public boolean hasNextByte() {
			if (curbuf >= lenbuf) {
				curbuf = 0;
				try {
					lenbuf = in.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return false;
			}
			return true;
		}
 
		private int readByte() {
			if (hasNextByte())
				return buffer[curbuf++];
			else
				return -1;
		}
 
		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}
 
		private void skip() {
			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
				curbuf++;
		}
 
		public boolean hasNext() {
			skip();
			return hasNextByte();
		}
 
		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (!isSpaceChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
 
		public int nextInt() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
 
		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
 
		public double nextDouble() {
			return Double.parseDouble(next());
		}
 
		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}
 
		public long[] nextLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}
 
		public char[][] nextCharMap(int n, int m) {
			char[][] map = new char[n][m];
			for (int i = 0; i < n; i++)
				map[i] = next().toCharArray();
			return map;
		}
	}
	}