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.util.*;
import java.io.*;
public class kkl {
    static long ans=0;
    static  long dp[];
    static  long w[];
    public static void main(String args[]) {
        FastReader sc = new FastReader();
        int n=sc.nextInt();
        int m=sc.nextInt();
        long mod=(long)Math.pow(10,9)+7;
        long dp[][]=new long[m+1][n+1];
        for(int i=1;i<=n;i++)
            dp[0][i]=1;
        for(int i=1;i<=m;i++){
            for(int j=1;j<=n;j++){
                long p=0,q=0;
                for(int k=0;k<=j;k++)
                    p=(p+dp[i-1][k])%mod;

                    q=(q+dp[i][j-1])%mod;

                dp[i][j]=(p+q)%mod;
            //System.out.print(dp[i][j]+" ");
            }
           // System.out.println();
        }

        System.out.println(dp[m][n]);

    }




    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            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;
        }
    }
}
class node{
    int val;
    int wt;
}