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.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

import javax.swing.plaf.basic.BasicInternalFrameTitlePane.MaximizeAction;

import java.util.*;
import java.io.*;
public class codeforces {
	static long[][] s;
public static long GCD(long a,long b) {

		return b==0?a:GCD(b, a%b);
	}
public static long	C(int a,int b) {
	int m=(int)1e9+7;
	if (s[a][b]>=0){
		return s[a][b];
	}
	else if(a<b|a<0|b<0){
		s[a][b]=0;
		return 0;
	}
	else if (a==b | b==0) {
		s[a][b]=1;
		return 1;
	}
	else {
		return s[a][b]=(C(a-1,b)%m+C(a-1, b-1)%m)%m;
	}
	
}
	public static void main(String[] args) throws IOException {
		
		Scanner sc=new Scanner(System.in);
		int b=sc.nextInt();
		int a=sc.nextInt();
		//String [][] a =new String [10][5];
		//String [][] b =a.clone();
		s=new long [2*a+b+2][b];
		for(long [] x : s) {
			Arrays.fill(x, -1);
		}
		System.out.println(C(2*a+b-1, b-1));
		//int n=s.nextInt();
		//int m=Math.(1,2);
		//System.out.println(m);
		//System.out.println(Arrays.toString(a));
		//for (int i=0;i<5;i++){
		//	System.out.println(i);
		//}
		//int[] arr = new int[5];
		//int[] arr2 = new int[5];
		//arr2= new int[] {1,3,1,1};
		//arr= new int[] {50,100,50,100};
		
	}
	static class Scanner {
		StringTokenizer st;
		BufferedReader br;
 
		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}
 
		public Scanner(FileReader r) {
			br = new BufferedReader(r);
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public String nextLine() throws IOException {
			return br.readLine();
		}
 
		public double nextDouble() throws IOException {
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if (x.charAt(0) == '-') {
				neg = true;
				start++;
			}
			for (int i = start; i < x.length(); i++)
				if (x.charAt(i) == '.') {
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				} else {
					sb.append(x.charAt(i));
					if (dec)
						f *= 10;
				}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg ? -1 : 1);
		}
 
		public boolean ready() throws IOException {
			return br.ready();
		}
 
	}

}