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.*;
import static java.lang.Math.*;

public class Task {
    static Reader reader;
    static PrintWriter out;

    static final long mod = (long)1e9 + 7;

    public static long C(long n, long r) {
        if (r > n - r) r = n - r;
        long val = 1;
        for (int i = 0; i < r; i++) {
            val = (val * (n - i)) % mod;
            val = (val * Math.modPow(i + 1, mod - 2, mod)) % mod;
        }
        return val;
    }

    public static void solve() throws IOException {
        int n = reader.nextInt();
        int m = reader.nextInt();
        out.println(C(n + 2 * m - 1, 2 * m));
    }

    public static void main(String[] args) throws IOException {
        reader = new Reader(System.in);
        out = new PrintWriter(System.out);

        solve();

        reader.close();
        out.close();
    }
}

class Math {
    public static long gcd(long a, long b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }

    public static long lcm(long a, long b) {
        return a * b / gcd(a, b);
    }

    public static long modPow(long a, long p, long mod) {
        if (p == 0) return 1;
        long v = modPow(a, p / 2, mod);
        v = (v * v) % mod;
        if (p % 2 == 1) v = (v * a) % mod;
        return v;
    }
}

class Reader implements Closeable {
    BufferedReader bufferedReader;
    StringTokenizer stringTokenizer;

    public Reader(InputStream source) throws IOException {
        bufferedReader = new BufferedReader(new InputStreamReader(source));
        stringTokenizer = new StringTokenizer("");
    }

    String next() throws IOException {
        while (!stringTokenizer.hasMoreTokens()) {
            stringTokenizer = new StringTokenizer(bufferedReader.readLine());
        }

        return stringTokenizer.nextToken();
    }

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

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

    @Override
    public void close() throws IOException {
        bufferedReader.close();
    }
}
