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.lang.*;
import java.lang.reflect.Array;
import java.io.*;
import java.math.*;
import java.text.DecimalFormat;
public class Rough{     
    static class InputReader { 
        private final InputStream stream;
	private final byte[] buf = new byte[8192];
	private int curChar, snumChars;
 	public InputReader(InputStream st) {
            this.stream = st;
	} 
	public int read() {
            if (snumChars == -1)
	 	throw new InputMismatchException();
            if (curChar >= snumChars) {
		curChar = 0;
                try {
                    snumChars = stream.read(buf);
		} 
                catch (IOException e) {
                    throw new InputMismatchException();
           	}
		if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
	}
        public int ni() {
            int c = read();
            while (isSpaceChar(c)) {
               	c = read();
            }
            int sgn = 1;
            if (c == '-') {
		sgn = -1;
		c = read();
            }
            int res = 0;
            do {
		res *= 10;
		res += c - '0';
		c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
	} 
	public long nl() {
            int c = read();
            while (isSpaceChar(c)) {
            c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
	} 
	public int[] nia(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
		a[i] = ni();
            }
            return a;
	} 
	public String rs() {
            int c = read();
            while (isSpaceChar(c)) {
		c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
		res.appendCodePoint(c);
                    c = read();
            } while (!isSpaceChar(c));
            return res.toString();
	}
	public String nextLine() {
            int c = read();
            while (isSpaceChar(c))
		c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        } 
	public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}
 
	private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
	} 
    }
    static PrintWriter w = new PrintWriter(System.out);
    static long mod1=998244353L,mod=1000000007L;
    public static long fact[]=new long[100005];
  
    public static void findFact(){
        fact[0]=1;
        for(int i=1;i<=100000;i++){
            fact[i]=(i*fact[i-1])%mod;
        }
    }
    static long modInverse(long a, long m){
      long num=m;
      long x=1;
      long power=a%mod;
      while(num>0){
          if(num%2==1){
              x=(x*power)%mod;
          }
         num>>=1;
         power=(power*power)%mod;
         
      }
      return x;
  }
  
public static long nCr(int n,int r){
    return (fact[n]*modInverse((fact[r]*fact[n-r])%mod,1000000005))%mod;
}
    public static void main (String[] args)throws IOException{      
        InputReader sc=new InputReader(System.in);
        findFact();
        int n=sc.ni(),m=sc.ni();
        w.println(nCr(2*m+n-1,n-1)%mod);
    	w.close();
    }
}