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 org.omg.Messaging.SyncScopeHelper;

import java.io.*;
import java.util.*;

public class Main {
    public static long ciel(long x,long y){
        long res=x/y;
        if(x%y!=0)res++;
        return res;
    }
    public static boolean check(String str){
        if(str.equals(".")||str.equals(",")||str.equals("!")||str.equals("?"))return true;
        return false;
    }
    public static long gcd(long u,long v){
        if(v==0)return u;
        return gcd(v, u%v);
    }
    static int n,m,mod= (int) (1e9+7);
    static long memo[][];
    public static long dp(int u,int v){
        if(v==0)return 1;
        if(u<v)return 0;
        if(memo[u][v]!=-1)return memo[u][v];
       return memo[u][v]=(dp(u-1, v-1)%mod+dp(u-1, v)%mod)%mod;

    }
    public static void main(String[] args) throws Exception {
        Scanner sc=new Scanner(System.in);
        PrintWriter pw=new PrintWriter(System.out);

        n=sc.nextInt();
        m=sc.nextInt();
        memo=new long[ (n+2*m)][ (n+1)];
        for(long []x:memo)Arrays.fill(x, -1);

        pw.println(dp(2*m+n-1, n-1)%mod);


        pw.close();
    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

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

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

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

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++)
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec)
                        f *= 10;
                }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }

        public boolean ready() throws IOException, IOException {
            return br.ready();
        }

    }
}
