You are given two integers n and m. Calculate the number of pairs of arrays (a, b) such that:

  * the length of both arrays is equal to m; 
  * each element of each array is an integer between 1 and n (inclusive); 
  * a_i ≤ b_i for any index i from 1 to m; 
  * array a is sorted in non-descending order; 
  * array b is sorted in non-ascending order. 



As the result can be very large, you should print it modulo 10^9+7.

Input

The only line contains two integers n and m (1 ≤ n ≤ 1000, 1 ≤ m ≤ 10).

Output

Print one integer – the number of arrays a and b satisfying the conditions described above modulo 10^9+7.

Examples

Input


2 2


Output


5


Input


10 1


Output


55


Input


723 9


Output


157557417

Note

In the first test there are 5 suitable arrays: 

  * a = [1, 1], b = [2, 2]; 
  * a = [1, 2], b = [2, 2]; 
  * a = [2, 2], b = [2, 2]; 
  * a = [1, 1], b = [2, 1]; 
  * a = [1, 1], b = [1, 1]. 
//package EducationalCFRd80D2;

import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class C_Two_Arrays {
	
	static long MOD = 1000000007;

	public static void main(String[] args) {
		MyScanner sc = new MyScanner();
	    PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
	    int N = sc.nextInt();
	    int M = sc.nextInt();
	    
	    //a, b, n
	    long[][] dp = new long[N+1][2*M+1];
	    for(int n = 1; n <= N; n++) {
	    	dp[n][1] = 1;
	    }
	    for(int m = 2; m <= 2*M; m++) {
	    	for(int n = 1; n <= N; n++) {
	    		//Curr dp value can come from dp[0...n][m - 1]
	    		dp[n][m] = dp[n][m - 1] + dp[n - 1][m];
	    		dp[n][m] %= MOD;
	    	}
	    }
	    long ans = 0;
	    for(int n = 1; n <= N; n++) {
	    	ans = (ans + dp[n][2*M])%MOD;
	    }
	    out.println(ans);
	    
	    out.close();
	}
	
	public static class MyScanner {
		BufferedReader br;
	    StringTokenizer st;
	 
	    public MyScanner() {
	       br = new BufferedReader(new InputStreamReader(System.in));
	    }
	 
	    String next() {
	    	while (st == null || !st.hasMoreElements()) {
	    		try {
	    			st = new StringTokenizer(br.readLine());
	            	
	    		} catch (IOException e) {
	    			e.printStackTrace();
	            }
	          }
	    	return st.nextToken();
	   }
	 
	   int nextInt() {
		   return Integer.parseInt(next());
	   }
	 
	   long nextLong() {
		   return Long.parseLong(next());
	   }
	 
	   double nextDouble() {
		   return Double.parseDouble(next());
	   }
	 
	   String nextLine(){
		   String str = "";
		   try {
			   str = br.readLine();
		   } catch (IOException e) {
			   e.printStackTrace();
		   }
		   return str;
	   }
	}
}