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.io.*;
public class Main{
	
	static final long p=1000000007;
	static long  x, y;
	
	static void gcd(long a, long b) {
		if(b==0) {
			x=1;
			y=0;
		}else {
			gcd(b,a%b);
			long t = x - a/b*y;
			x=y;
			y=t;
		}
			
		
	}
	
	static long inv(long a) {
		gcd(a,p);
		if(x<0)
			 x+=p;
		return x;
	}
	
	static long nCr(long n, long r) 
	{ 
		if(r>n/2)
			r=n-r;
	    long a=1, b=1;
	    for(int i=0; i<r; i++) {
	    	a=a*(n-i)%p;
	    	b=b*(i+1)%p;
	    }
	    return (a*inv(b))%p;
	} 
	  

	
	 public static void main (String args[])throws IOException{
        Scanner sc = new Scanner();
        PrintWriter out = new PrintWriter(System.out);
        
        long n=sc.nextLong(), m=sc.nextLong();
       
        out.println(nCr(2*m+n-1,n-1));
        out.flush();
    }	
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 static class Scanner {
			BufferedReader br;
			StringTokenizer st;
	 
			Scanner() {
				br = new BufferedReader(new InputStreamReader(System.in));
			}
	 
			Scanner(String fileName) throws FileNotFoundException {
				br = new BufferedReader(new FileReader(fileName));
			}
	 
			String next() throws IOException {
				while (st == null || !st.hasMoreTokens())
					st = new StringTokenizer(br.readLine());
				return st.nextToken();
			}
	 
			String nextLine() throws IOException {
				return br.readLine();
			}
	 
			int nextInt() throws IOException {
				return Integer.parseInt(next());
			}
	 
			long nextLong() throws NumberFormatException, IOException {
				return Long.parseLong(next());
			}
	 
			double nextDouble() throws NumberFormatException, IOException {
				return Double.parseDouble(next());
			}
	 
			boolean ready() throws IOException {
				return br.ready();
			}
	 
		}
	 
		static void sort(int[] a) {
			shuffle(a);
			Arrays.sort(a);
		}
	 
		static void shuffle(int[] a) {
			int n = a.length;
			Random rand = new Random();
			for (int i = 0; i < n; i++) {
				int tmpIdx = rand.nextInt(n);
				int tmp = a[i];
				a[i] = a[tmpIdx];
				a[tmpIdx] = tmp;
			}
		}
}


