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 我不知道我是谁
import java.io.*;
import java.util.*;
public class scratch_18{


    static class Reader {
        static BufferedReader reader;
        static StringTokenizer tokenizer;

        static void init(InputStream input) {
            reader = new BufferedReader(
                    new InputStreamReader(input));
            tokenizer = new StringTokenizer("");
        }

        static String next() throws IOException {
            while (!tokenizer.hasMoreTokens()) {
                //TODO add check for eof if necessary
                tokenizer = new StringTokenizer(
                        reader.readLine());
            }
            return tokenizer.nextToken();
        }

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

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

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



    public static void main(String[] args)  throws IOException {
        Reader.init(System.in);
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
        int n= Reader.nextInt();
        int m= Reader.nextInt();
        long mod=(long)(1e9+7);
        long dp[][]= new long[2*m][n+1];    // dp(i)(j) will denote the number of subsequences of length i ending at j
        for (int i = 0; i <2*m ; i++) {
            Arrays.fill(dp[i],1);
        }

        for (int i = 1; i <2*m ; i++) {
            for (int j = 1; j <=n ; j++) {
                long sum=0;
                for (int k = 1; k <=j ; k++) {
                    sum=(sum%mod+dp[i-1][k]%mod)%mod;
                }
                dp[i][j]=sum;
            }
        }
long ans=0;
        for (int i = 1; i <=n ; i++) {
            ans= (ans%mod+dp[2*m-1][i]%mod)%mod;
        }
        out.append(ans+"\n");













        out.flush();
        out.close();
    }
}








