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 C {
    static int n, m, mod = (int) 1e9 + 7;
    static int[][] dp;

    static int solve(int indx, int cur) {
        if (indx == m + m) {
            return 1;
        }
        if (dp[indx][cur] != -1) {
            return dp[indx][cur];
        }
        dp[indx][cur] = 0;
        for (int i = cur; i < n; i++) {
            dp[indx][cur] = ((dp[indx][cur] + solve(indx + 1, i)) % mod);
        }//fora
        return dp[indx][cur];
    }//solve

    public static void main(String[] args) throws Exception {
        FastReader in = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        n = in.nextInt();
        m = in.nextInt();
        dp = new int[m + m][n + 1];
        fill();
        out.println(solve(0, 0));
        out.flush();
    }//psvm

    static void fill() {
        for (int i = 0; i < m + m; i++) {
            for (int j = 0; j < n + 1; j++) {
                dp[i][j] = -1;
            }
        }
    }//fill

    static class FastReader {

        BufferedReader br;
        StringTokenizer st;

        FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        FastReader(File f) {
            try {
                br = new BufferedReader(new FileReader(f));
            } catch (FileNotFoundException x) {
                System.out.println(x);
            }
        }

        String next() throws IOException {
            while (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(br.readLine());
            }
            return st.nextToken();
        }

        String nextLine() throws IOException {
            return br.readLine();
        }

        int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        boolean hasNext() throws IOException {
            String s = br.readLine();
            if (s == null) {
                return false;
            }
            st = new StringTokenizer(s);
            return true;
        }
    }
}//class
