Problem: Let's assume that set S consists of m distinct intervals [l1, r1], [l2, r2], ..., [lm, rm] (1 ≤ li ≤ ri ≤ n; li, ri are integers).

Let's assume that f(S) is the maximum number of intervals that you can choose from the set S, such that every two of them do not intersect. We assume that two intervals, [l1, r1] and [l2, r2], intersect if there is an integer x, which meets two inequalities: l1 ≤ x ≤ r1 and l2 ≤ x ≤ r2.

Sereja wonders, how many sets S are there, such that f(S) = k? Count this number modulo 1000000007 (109 + 7).

Input

The first line contains integers n, k (1 ≤ n ≤ 500; 0 ≤ k ≤ 500).

Output

In a single line, print the answer to the problem modulo 1000000007 (109 + 7).

Examples

Input

3 1


Output

23


Input

3 2


Output

32


Input

2 0


Output

1


Input

2 2


Output

2

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.*;
import java.util.*;

public class Main {
    static int MOD = (int)1e9 + 7;

    public void run() {
        try {
            int n = reader.nextInt();
            int m = reader.nextInt();
            int[] pow = new int[n + 1];
            pow[0] = 1;
            for (int i = 1; i <= n; ++ i) {
                pow[i] = (pow[i - 1] << 1) % MOD;
            }
            int[][] ways = new int[m + 1][1];
            ways[0][0] = 1;
            for (int i = 0; i < n; ++ i) {
                int[][] newWays = new int[m + 1][i + 2];
                for (int maximum = 0; maximum <= m && maximum <= i; ++ maximum) {
                    for (int last = 0; last <= i; ++ last) {
                        long value = ways[maximum][last];
                        newWays[maximum][last] = add(newWays[maximum][last], (int)value);
                        newWays[maximum][last] = add(newWays[maximum][last], (int)(value * (pow[last] - 1) % MOD));
                        if (maximum + 1 <= m) {
                            newWays[maximum + 1][i + 1] = add(newWays[maximum + 1][i + 1], (int)(value * (pow[i + 1] - pow[last]) % MOD));
                        }
                    }
                }
                ways = newWays;
            }
            int result = 0;
            for (int last = 0; last <= n; ++ last) {
                result = add(result, ways[m][last]);
            }
            writer.println(result);
        } catch (IOException ex) {
        }
        writer.close();
    }

    int add(int x, int a) {
        if (a < 0) {
            a += MOD;
        }
        x += a;
        if (x >= MOD) {
            x -= MOD;
        }
        return x;
    }

    Main() {
        reader = new InputReader(System.in);
        writer = new PrintWriter(System.out);
    }

    public static void main(String[] args) {
        new Main().run();
    }

    private void debug(Object...os) {
        System.err.println(Arrays.deepToString(os));
    }

    private InputReader reader;
    private PrintWriter writer;
}

class InputReader {
    InputReader(InputStream in) {
        reader    = new BufferedReader(new InputStreamReader(in));
        tokenizer = new StringTokenizer("");
    }

    private String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }

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

    private BufferedReader  reader;
    private StringTokenizer tokenizer;
}