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.*;

public class Main {
	static int P = (int)1e9 + 7;
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		int n = sc.nextInt();
		int m = sc.nextInt();
		
		int a = 2*m + n - 1;
		int b = n-1;
		
		long[] aa = new long[1100];
		long[] bb = new long[1100];
		aa[0] = 1;
		bb[0] = 1;
		for(int i=1;i<aa.length;i++) {
			aa[i] = aa[i-1] * i % P;
			bb[i] = bb[i-1] * fp(i, P-2) % P;
		}
		
		System.out.println(aa[a] * bb[a-b] % P * bb[b] % P);
	}
	static long fp(int a, int p) {
		if(p == 0)
			return 1;
		long num = fp(a, p/2);
		if(p % 2 == 0)
			return num * num % P;
		else
			return num * num % P * a % P;
	}
}