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.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;

public class Main {
	public static class FastReader {
			BufferedReader br;
			StringTokenizer root;
			
	 
			public FastReader() {
				br = new BufferedReader(new InputStreamReader(System.in));
			}
	 
			String next() {
				while (root == null || !root.hasMoreTokens()) {
					try {
						root = new StringTokenizer(br.readLine());
					} catch (Exception addd) {
						addd.printStackTrace();
					}
				}
				return root.nextToken();
			}
	 
			int nextInt() {
				return Integer.parseInt(next());
			}
	 
			double nextDouble() {
				return Double.parseDouble(next());
			}
	 
			long nextLong() {
				return Long.parseLong(next());
			}
	 
			String nextLine() {
				String str = "";
				try {
					str = br.readLine();
				} catch (Exception addd) {
					addd.printStackTrace();
				}
				return str;
			}
		}
	 
	public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
	public static FastReader sc = new FastReader();
 
	static long mod = (long) (1e9+7),MAX=(long)(1e6+10);
	static List<Integer>[] edges;
    static int[][] dp;
    
	public static void main(String[] args) throws IOException{

		int n = sc.nextInt();
		int m = sc.nextInt();
		dp = new int[2*m+1][n+1];
		for(int i=0;i<dp.length;++i) Arrays.fill(dp[i], -1);
		out.print(f(2*m,n));
		out.close();
	}

	private static int f(int i, int j) {
		if(i == 1) return Math.max(0, j);
		if(dp[i][j] != -1) return dp[i][j];
		int ans = 0;
		for(int k=1;k<=j;++k) {
			ans = ans + f(i-1,k);
			if(ans >= mod) ans-=mod;
		}
		return dp[i][j] = ans;
	}

}
			