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]. 
//Created by Aminul on 1/21/2020.

import java.io.*;
import java.util.*;

import static java.lang.Math.*;

public class C {
    static int dp[][][], n, m, mod = (int) 1e9 + 7;

    public static void main(String[] args) throws Exception {
        new Thread(null ,new Runnable(){
            public void run(){
                try{solveIt();} catch(Exception e){e.printStackTrace(); System.exit(1);}
            }
        },"Main",1<<28).start();
    }
    
    public static void solveIt() throws Exception {
        Scanner in = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        n = in.nextInt();
        m = in.nextInt();
        dp = new int[m + 1][n + 1][n + 1];
        for (int a[][] : dp) for (int b[] : a) Arrays.fill(b, -1);
        int res = solve(1, n, 0);
        pw.println(res);
        pw.close();
    }

    static int solve(int a, int b, int pos) {
        if (a < 1 || a > n || b < 1 || b > n || a > b) return 0;
        if (pos >= m) return 1;
        if (dp[pos][a][b] != -1) return dp[pos][a][b];
        int res = solve(a, b, pos + 1);
        res += solve(a + 1, b, pos);
        if (res >= mod) res -= mod;
        res += solve(a, b - 1, pos);
        if (res >= mod) res -= mod;
        res -= solve(a + 1, b - 1, pos);
        if(res < 0) res += mod;
        return dp[pos][a][b] = res;
    }

    static void debug(Object... obj) {
        System.err.println(Arrays.deepToString(obj));
    }
}