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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.StringTokenizer;
import static java.lang.Long.bitCount;

public class Main {

  public static void main(String[] args) {
    FastScanner in = new FastScanner();
    int MOD = (int)Math.pow(10, 9)+7;
    int n, m; n = in.nextInt();
    m = in.nextInt();
    Long [][]dp = new Long[2*m+1][n+1];
    m = 2*m;
    for(int i=0; i<=m; ++i){
      Arrays.fill(dp[i], 0L);
    }
    dp[1][0] = 0L;
    for(int i=1; i<=n; ++i){
      dp[1][i] = i + dp[1][i-1];
      dp[1][i] %= MOD;
    }
    for(int i=2; i<=m; ++i){
      for(int j=1; j<=n; ++j){
        if(j == 1) dp[i][j] = 1L;
        else dp[i][j] = dp[i-1][j] + dp[i][j-1];
        dp[i][j] %= MOD;
      }
    }
    System.out.println((dp[m][n]-dp[m][n-1]+MOD)%MOD);
  }

  static void sort(int[] a) {
    ArrayList<Integer> l=new ArrayList<>();
    for (int i:a) l.add(i);
    Collections.sort(l);
    for (int i=0; i<a.length; i++) a[i]=l.get(i);
  }

  static class FastScanner {
    BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer st=new StringTokenizer("");
    String next() {
      while (!st.hasMoreTokens())
        try {
          st=new StringTokenizer(br.readLine());
        } catch (IOException e) {
        e.printStackTrace();
        }
      return st.nextToken();
    }

    int nextInt() {
      return Integer.parseInt(next());
    }
    int[] readArray(int n) {
      int[] a=new int[n];
      for (int i=0; i<n; i++) a[i]=nextInt();
      return a;
    }
    long nextLong() {
      return Long.parseLong(next());
    }

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