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.*;
import java.io.*;
public class C {
	
	static long mod = 1000000007;
	public static void main(String[] args) {
		FastScanner sc = new FastScanner();
		int n = sc.nextInt();
		int m = sc.nextInt();
		long[][] dp = new long[m][n+1];
		for(int i = 1; i <= n; i++) {
			dp[0][i] = 1;
		}
		for(int i = 1; i < m; i++) {
			for(int j = 1; j <= n; j++) {
				for(int k = 1; k <= j; k++) {
					dp[i][j] = (dp[i][j] + dp[i-1][k]) % mod;
				}
			}
		}
		long res = 0;
		for(int a = 1; a <= n; a++) {
			for(int b = a; b <= n; b++) {
				long add = (dp[m-1][a] * dp[m-1][n-b+1]) % mod;
				res = (res + add) % mod;
			}
		}
		System.out.println(res);
	}
	
	static class FastScanner {
		public BufferedReader reader;
		public StringTokenizer tokenizer;
		public FastScanner() {
			reader = new BufferedReader(new InputStreamReader(System.in), 32768);
			tokenizer = null;
		}
		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
		public double nextDouble() {
			return Double.parseDouble(next());
		}
		public String nextLine() {
			try {
				return reader.readLine();
			} catch(IOException e) {
				throw new RuntimeException(e);
			}
		}
	}


}
