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.nio.charset.Charset;
import java.io.*;
import java.nio.charset.StandardCharsets;
import java.util.*;

public class Main {

    private static void solve(MyScanner in) throws IOException {

    }

    private static long f(int n, int m, int biggest, final long MOD) {
        if (m == 0) {
            return 1;
        }
        long[][] dp = new long[m + 1][n + 1];
        long[][] sum = new long[m + 1][n + 1];

        for (int i = biggest; i <= n; i++) {
            dp[1][i] = 1;
            sum[1][i] = n - i + 1;
        }
        for (int i = 2; i <= m; i++) {
            for (int j = biggest; j <= n; j++) {
                // sum j...n
                dp[i][j] = sum[i - 1][j];
            }
            long s = 0;
            for (int j = n; j >= biggest; j--) {
                s += dp[i][j];
                s %= MOD;
                sum[i][j] = s;
            }
        }
        return sum[m][biggest];
    }

    public static void main(String[] args) throws IOException {
        MyScanner in = new MyScanner(System.in, Character::isWhitespace, StandardCharsets.UTF_8);
        int n = in.nextInt();
        int m = in.nextInt();
        final long MOD = 1000 * 1000 * 1000 + 7;
        long ans = 0;
        for (int biggest = 1; biggest <= n; biggest++) {
            // System.out.println(biggest + " " + f(n, m, biggest, MOD) + " " + f(n, m - 1, n - biggest + 1, MOD));
            ans += f(n, m, biggest, MOD) * f(n, m - 1, n - biggest + 1, MOD) % MOD;
        }
        System.out.println(ans % MOD);
        in.close();
    }
}

interface Checker {
    boolean isWhitespace(char c);
}

class MyScanner implements AutoCloseable {
    private Reader in;
    private final Checker checker;
    private int cur;

    public MyScanner(String s, Checker checker) throws IOException {
        this.checker = checker;
        in = new BufferedReader(new StringReader(s));
        nextChar();
    }

    public MyScanner(InputStream inputStream, Checker checker, Charset charset) throws IOException {
        this.checker = checker;
        in = new BufferedReader(new InputStreamReader(inputStream, charset));
        nextChar();
    }

    public MyScanner(File file, Checker checker, Charset charset) throws FileNotFoundException, IOException {
        this.checker = checker;
        in = new BufferedReader(new InputStreamReader(new FileInputStream(file), charset));
        nextChar();
    }

    public boolean hasNextChar() {
        return cur != -1;
    }

    public char nextChar() throws IOException {
        char ans = (char) cur;
        cur = in.read();
        return ans;
    }

    public void skipWhitespaces() throws IOException {
        while (hasNextChar() && checker.isWhitespace((char) cur)) {
            nextChar();
        }
    }

    public boolean hasNext() throws IOException {
        skipWhitespaces();
        return hasNextChar();
    }

    public String next() throws IOException {
        skipWhitespaces();
        StringBuilder builder = new StringBuilder();
        while (hasNextChar() && !checker.isWhitespace((char) cur)) {
            builder.append(nextChar());
        }
        return builder.toString();
    }

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

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

    public boolean isEOL() throws IOException {
        while (hasNextChar() && cur != '\n' && cur != '\r' && checker.isWhitespace((char) cur)) {
            nextChar();
        }
        return !hasNextChar() || cur == '\n' || cur == '\r';
    }

    public void skipEOL() throws IOException {
        if (cur == '\r') {
            nextChar();
        }
        if (cur == '\n') {
            nextChar();
        }
    }

    public void close() throws IOException {
        in.close();
    }
}