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 EducationalRound80;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class ProblemC {
    public static void print(long dp[][]){
        for(int i=1;i<dp.length;i++){
            for(int j=1;j<dp[i].length;j++){
                System.out.print(dp[i][j]+" ");
            }
            System.out.println();
        }
    }
    public static void main(String[] args)throws IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        String line[]=br.readLine().split(" ");
        int n=Integer.parseInt(line[0]);
        int m=Integer.parseInt(line[1]);
        int mod=1000000007;
        long dp[][]=new long[n+1][2*m+1];
        for(int i=1;i<=n;i++){
            dp[i][1]=i;
        }
        for(int j=1;j<=2*m;j++){
            dp[1][j]=1;
        }
        long sum=1;
        for(int i=2;i<=n;i++){
            for(int j=2;j<=2*m;j++){
                dp[i][j]=(dp[i-1][j]+dp[i][j-1])%mod;
            }
        }
//        print(dp);
        System.out.println(dp[n][2*m]);
    }
}
