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]. 
import java.io.*;
import java.lang.reflect.Array;
import java.util.*;

import static java.lang.Math.ceil;


public class Solver {
    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(System.out);
        int n = nextInt();
        int m = nextInt();
        long a[][] = new long[2 * m][n];
        for (int i = 0; i < n; i++) {
            a[0][i] = 1;
        }
        for (int i = 1; i < 2 * m; i++) {
            for (int j = 0; j < n; j++) {
                for (int k = 0; k <= j; k++) {
                    a[i][j] += a[i - 1][k];
                }
                a[i][j] %= mod;
            }
        }
        long ans = 0;
        for (int i = 0; i < n; i++) {
            ans = (ans +a[2 * m - 1][i]) % mod;
        }
        pw.println(ans);
        pw.close();
    }

    static PrintWriter pw;
    static StringTokenizer st = new StringTokenizer("");
    static BufferedReader br;

    static long mod = 1_000_000_007;

    static String next() throws IOException {
        while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
}

class S {
    long max, i;

    public S(long max, long i) {
        this.max = max;
        this.i = i;
    }
}

class CS implements Comparator<S> {
    public int compare(S o1, S o2) {
        return Long.compare(o1.max, o2.max);
    }
}