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.*;
import java.util.*;
public class edu3{
	public static void main(String []args)throws IOException{
		
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	
			String[] temp=br.readLine().split("\\s");
			int n=Integer.parseInt(temp[0]);
			int m=Integer.parseInt(temp[1]);
		int[] a=new int[n];
		int mod=(int)1e9 +7;
		Arrays.fill(a,1);
		for(int i=1;i<2*m;i++){
			for(int j=1;j<n;j++){
				a[j]=(a[j]+a[j-1])%mod;
			}
			
		}
		int sum=0;
		for(int s:a){
			sum=(sum+s)%mod;
		}
		
		System.out.println(sum);

		
	}

		
}