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 c {
	static Scanner in=new Scanner(System.in);
	static long[][] ncr;
	public static void main(String[] args) {
		int mod=1000000007;
		ncr=numCombinations(1011,mod);
		int n=in.nextInt(),m=in.nextInt();
		//just care about last number. a must go small->big, and b must go small at the back to big at the front. so iterate over the last number of the array and do some math
		long ans=0;

		for(int lasta=1;lasta<=n;lasta++) for(int startb=lasta;startb<=n;startb++){
			ans+=fun(m,lasta-1)*fun(m,n-startb);
			ans%=mod;
		}
		System.out.println(ans);
	}
	private static long fun(int size, int count) {//stars and bars
		return ncr[count+size-1][count];
	}

	public static long[][]  numCombinations(int max, int mod){
		long[][] ans=new long[max][max];
		for(int i=0;i<max;i++)ans[i][0]=1;
		for(int i=1;i<max;i++)for(int j=1;j<max;j++)ans[i][j]=(ans[i-1][j]+ans[i-1][j-1])%mod;
		return ans;
	}

}
