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 main;
import java.io.*;
import java.util.*;
import java.lang.*;
import java.math.*;
public class Submission {
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter (System.out);
        //BufferedReader reader = new BufferedReader(new InputStreamReader(new FileInputStream("input.txt")));
        StringTokenizer st = new StringTokenizer(reader.readLine()," ");
        int n = Integer.parseInt(st.nextToken());
        int m = Integer.parseInt(st.nextToken());
        //answer is 2m+n-1 choose 2m
        long prime = 1000000007;
        long answer0=1;
        long fact=1;
        for (int i=0;i<2*m;i++) answer0=(answer0*(2*m+n-i-1))%prime;
        for (int i=0;i<2*m;i++) fact=(fact*(i+1))%prime;
        long b = new BigInteger(Long.toString(fact)).modInverse(new BigInteger(Long.toString(prime))).longValue();
        out.println((answer0*b)%prime);
        reader.close();
        out.close();
    }
}