Problem: In "Takahashi-ya", a ramen restaurant, basically they have one menu: "ramen", but N kinds of toppings are also offered. When a customer orders a bowl of ramen, for each kind of topping, he/she can choose whether to put it on top of his/her ramen or not. There is no limit on the number of toppings, and it is allowed to have all kinds of toppings or no topping at all. That is, considering the combination of the toppings, 2^N types of ramen can be ordered.

Akaki entered Takahashi-ya. She is thinking of ordering some bowls of ramen that satisfy both of the following two conditions:

* Do not order multiple bowls of ramen with the exactly same set of toppings.
* Each of the N kinds of toppings is on two or more bowls of ramen ordered.



You are given N and a prime number M. Find the number of the sets of bowls of ramen that satisfy these conditions, disregarding order, modulo M. Since she is in extreme hunger, ordering any number of bowls of ramen is fine.

Constraints

* 2 \leq N \leq 3000
* 10^8 \leq M \leq 10^9 + 9
* N is an integer.
* M is a prime number.

Input

Input is given from Standard Input in the following format:


N M


Output

Print the number of the sets of bowls of ramen that satisfy the conditions, disregarding order, modulo M.

Examples

Input

2 1000000007


Output

2


Input

3 1000000009


Output

118


Input

50 111111113


Output

1456748


Input

3000 123456791


Output

16369789

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskE solver = new TaskE();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskE {
        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            int n = in.nextInt();
            int mod = in.nextInt();

            int[][] choose = new int[n + 10][n + 10];
            int[][] stirling = new int[n + 10][n + 10];
            for (int i = 0; i <= n + 9; i++) {
                choose[i][0] = 1;
                for (int j = 1; j <= i; j++) {
                    choose[i][j] = choose[i - 1][j - 1] + choose[i - 1][j];
                    if (choose[i][j] >= mod) {
                        choose[i][j] -= mod;
                    }
                }
                stirling[i][0] = (i == 0) ? 1 : 0;
                for (int j = 1; j <= i; j++) {
                    stirling[i][j] = (int) ((stirling[i - 1][j - 1] + 1L * stirling[i - 1][j] * j) % mod);
                }
            }
            int[] pow2 = new int[n * n + 1];
            pow2[0] = 1;
            for (int i = 1; i < pow2.length; i++) {
                pow2[i] = pow2[i - 1] * 2;
                if (pow2[i] >= mod) {
                    pow2[i] -= mod;
                }
            }

            int[] dp = new int[n + 1];
            for (int k = 0; k <= n; k++) {
                for (int used = 0; used <= k; used++) {
//                long mul = MathUtils.modPow(2, (n - k) * used, mod);
                    long sum = stirling[k + 1][used + 1];
                    long mul = pow2[(n - k) * used];
//                for (int x = 0; x <= k; x++) {
//                    sum += 1L * choose[k][x] * stirling[x][used] % mod;
//                }
                    dp[k] = (int) ((dp[k] + sum % mod * mul) % mod);
//                System.err.println(k + " " + used + " " + sum % mod);
                }
            }
            long ans = 0;
            for (int bits = 0; bits <= n; bits++) {
                long mul = MathUtils.modPow(2, MathUtils.modPow(2, n - bits, mod - 1), mod);
                mul = mul * choose[n][bits] % mod;
                mul = mul * dp[bits] % mod;
                ans += (bits % 2 == 0) ? mul : (-mul);
            }
            out.println((ans % mod + mod) % mod);
        }

    }

    static class MathUtils {
        public static int modPow(int a, long b, int mod) {
            while (a < 0) {
                a += mod;
            }
            int res = 1;
            while (b > 0) {
                if ((b & 1) != 0) {
                    res = (int) ((long) res * a % mod);
                }
                a = (int) ((long) a * a % mod);
                b >>>= 1;
            }
            return res;
        }

    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
        }

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

        public String next() {
            while (st == null || !st.hasMoreElements()) {
                String line = null;
                try {
                    line = br.readLine();
                } catch (IOException e) {
                }
                st = new StringTokenizer(line);
            }
            return st.nextToken();
        }

    }
}