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.io.File;
import java.util.Scanner;
import java.util.StringTokenizer;

public class p041 {
	public static void main(String args[]) throws Exception {
		StringTokenizer stok = new StringTokenizer(new Scanner(System.in).useDelimiter("\\A").next());
		StringBuilder sb = new StringBuilder();
		int n = Integer.parseInt(stok.nextToken());
		int m = Integer.parseInt(stok.nextToken());
		long mod = (long)1e9+7;
		long[] dp = new long[n+1];
		for(int i=1;i<=n;i++) dp[i]=1;
		for(int i=2;i<=m;i++) {
			for(int j=n;j>=1;j--) {
				for(int k=j-1;k>=1;k--) dp[j]=(dp[j]+dp[k])%mod;
			}
		}
		long tot = 0;
		for(int i=1;i<=n;i++) {
			for(int j=1;j<=n-i+1;j++)
			tot = (tot+(dp[i]*dp[j])%mod)%mod;
		}
		System.out.println(tot);
	}
}