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 Abc {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int m = in.nextInt();
		long sumA[][] = new long[n][2 * m];
		for(int j = 2 * m - 1; j >= 0; j --) {
			for(int i = 0; i < n; i++) {
				if(j == 2 * m - 1) {
					sumA[i][j] = 1;
				} else {
					sumA[i][j] = sumA[i][j + 1];
				}
			}
			for(int i = n - 2; i >= 0; i --) {
				sumA[i][j] += sumA[i + 1][j];
				sumA[i][j] %= mod;
			}
		}
		//print(sumA);
		System.out.println(sumA[0][0]);
	}
	public static void print(long ar[][]) {
		for(int i = 1; i < ar.length; i++) {
			System.out.println(Arrays.toString(ar[i]));
		}
	}
	long sum = 0;
	static long mod = 1000000007;
}