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]. 
// practice with rainboy
import java.io.*;
import java.util.*;

public class CF1288C extends PrintWriter {
	CF1288C() { super(System.out, true); }
	Scanner sc = new Scanner(System.in);
	public static void main(String[] $) {
		CF1288C o = new CF1288C(); o.main(); o.flush();
	}

	static final int MD = 1000000007;
	int d_, x_, y_;
	void gcd_(int a, int b) {
		if (b == 0) {
			d_ = a; x_ = 1; y_ = 0;
		} else {
			gcd_(b, a % b);
			int t = x_ - a / b * y_; x_ = y_; y_ = t;
		}
	}
	int inv(int a) {
		gcd_(a, MD);
		if (x_ < 0)
			x_ += MD;
		return x_;
	}
	int choose(int n, int k) {
		long p = 1, q = 1;
		for (int i = 0; i < k; i++) {
			p = p * (n - i) % MD;
			q = q * (i + 1) % MD;
		}
		return (int) (p * inv((int) q) % MD);
	}
	void main() {
		int n = sc.nextInt();
		int m = sc.nextInt();
		println(choose(m * 2 + n - 1, n - 1));
	}
}
