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 E80C {
	public static void main(String args[]) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		int mod = 1000000007;
		int[][] dp = new int[21][1001];
		Arrays.fill(dp[0],1);

		for(int i=1; i<21; i++) {
			for(int j=1; j<1001; j++) {
				if(j == 1) 
					dp[i][j] = 1;
				else {
					int sum = 0;
					for(int k=1; k<=j; k++) {
						sum = (sum + dp[i-1][k]) % mod;
					}
					dp[i][j] = sum;
				}
			}
		}
		System.out.println(dp[2*m][n]);
	}
}