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]. 
//189301019.akshay
import java.io.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.Scanner; 
import java.util.Random;
import java.util.Arrays;
import java.util.StringTokenizer; 
import java.util.ArrayList;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Collections;

public class D 
{ 
	static long mod = (long)(1e9+7);
    public static void main(String[] args) 
	{ 
		FastReader sc=new FastReader(); 
		StringBuffer ans=new StringBuffer();
		int test=1;
		long fact[]=new long[2005];
		
		fact[0]=fact[1]=1;
		for(int i=2;i<=2000;i++) {
			fact[i]= (fact[i-1]*i)%mod;
		}
		
		while(test-->0)
		{
			int n=sc.nextInt();
			int m=sc.nextInt();
			
			long num = fact[n+(2*m)-1];
			long den = (fact[2*m] * fact[n-1])%mod;
			long res = (binexp(den,mod-2,mod)*num)%mod;
			
			ans.append(res+"\n");
			
			
		
		}
		
	    System.out.print(ans);
	} 
    
    static long binexp(long p,long q,long mod) {
    	if(q == 0) {
    		return 1l;
    	}
    	
    	long temp =binexp(p,q/2,mod);
    	temp=(temp *temp)%mod;
    	
    	if(q%2 == 1) temp=(temp*p)%mod;
    	
    	return temp;
    	
    }
    
    static final Random random=new Random();
    
	static void ruffleSort(int[] a) {
		int n=a.length;//shuffle, then sort 
		for (int i=0; i<n; i++) {
			int oi=random.nextInt(n), temp=a[oi];
			a[oi]=a[i]; a[i]=temp;
		}
		Arrays.sort(a);
	}
	
	static void ruffleSort(long[] a) {
		int n=a.length;//shuffle, then sort 
		for (int i=0; i<n; i++) {
			int oi=random.nextInt(n);
			long temp=a[oi];
			a[oi]=a[i]; a[i]=temp;
		}
		Arrays.sort(a);
	}
	
	static class FastReader 
	{ 
		BufferedReader br; 
		StringTokenizer st; 

		public FastReader() 
		{ 
			br = new BufferedReader(new
					InputStreamReader(System.in)); 
		} 

		String next() 
		{ 
			while (st == null || !st.hasMoreElements()) 
			{ 
				try
				{ 
					st = new StringTokenizer(br.readLine()); 
				} 
				catch (IOException e) 
				{ 
					e.printStackTrace(); 
				} 
			} 
			return st.nextToken(); 
		} 

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

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

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

		String nextLine() 
		{ 
			String str = ""; 
			try
			{ 
				str = br.readLine(); 
			} 
			catch (IOException e) 
			{ 
				e.printStackTrace(); 
			} 
			return str; 
		} 
	} 


} 
