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:
// package arc.arc096;

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n = in.nextInt();
        MOD = in.nextInt();
        prec(12000);

        long[][] stir = stirlingSecond(n, MOD);

        long[] pow2 = new long[n+10];
        pow2[0] = 1;
        for (int i = 1; i < pow2.length ; i++) {
            pow2[i] = pow2[i-1] * 2 % MOD;
        }
        long[] other2 = new long[n+10];
        other2[0] = 2;
        for (int i = 1 ; i < other2.length ; i++) {
            other2[i] = (other2[i-1] * other2[i-1]) % MOD;
        }

        long[] p2p = new long[n+10];

        long total = 0;
        for (int i = 1 ; i <= n ; i++) {
            long o2 = other2[n-i];
            long p2 = pow2[n-i];

            p2p[0] = 1;
            for (int j = 1 ; j < p2p.length ; j++) {
                p2p[j] = p2p[j-1] * p2 % MOD;
            }

            long co = comb(n, i);
            long sum = 0;
            for (int j = 1 ; j <= i ; j++) {
                long way = stir[i][j] % MOD;

                // one of them is zero
                sum += way * j % MOD * p2p[j-1] % MOD;

                // all of them is one
                sum += way * p2p[j] % MOD;

                sum %= MOD;
            }
            sum = sum * co % MOD * o2 % MOD;

            if (i % 2 == 1) {
                total += sum;
            } else {
                total += MOD - sum;
            }
        }
        total %= MOD;

        out.println((other2[n] + MOD - total) % MOD);
        out.flush();
    }

    static int MOD = 1000000007;

    public static long[][] stirlingSecond(int n, long mod) {
        long[][] ret = new long[n+1][n+1];
        ret[0][0] = 1;
        for (int i = 1 ; i <= n ; i++) {
            for (int j = 1 ; j <= i ; j++) {
                ret[i][j] += ret[i-1][j-1];
                ret[i][j] += ret[i-1][j] * j;
                ret[i][j] %= mod;
            }
        }
        return ret;
    }

    static long pow(long a, long x) {
        long res = 1;
        while (x > 0) {
            if (x % 2 != 0) {
                res = (res * a) % MOD;
            }
            a = (a * a) % MOD;
            x /= 2;
        }
        return res;
    }

    static long inv(long a) {
        return pow(a, MOD - 2) % MOD;
    }

    static long[] _fact;
    static long[] _invfact;

    static long comb(long ln, long lr) {
        int n = (int) ln;
        int r = (int) lr;
        if (n < 0 || r < 0 || r > n) {
            return 0;
        }
        if (r > n / 2) {
            r = n - r;
        }
        return (((_fact[n] * _invfact[n - r]) % MOD) * _invfact[r]) % MOD;
    }

    static void prec(int n) {
        _fact = new long[n + 1];
        _invfact = new long[n + 1];
        _fact[0] = 1;
        _invfact[0] = 1;
        for (int i = 1; i <= n; i++) {
            _fact[i] = _fact[i - 1] * i % MOD;
            _invfact[i] = inv(_fact[i]);
        }
    }


    public static void debug(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }

    public static class InputReader {
        private static final int BUFFER_LENGTH = 1 << 12;
        private InputStream stream;
        private byte[] buf = new byte[BUFFER_LENGTH];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        private int next() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public char nextChar() {
            return (char) skipWhileSpace();
        }

        public String nextToken() {
            int c = skipWhileSpace();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char) c);
                c = next();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public int nextInt() {
            return (int) nextLong();
        }

        public long nextLong() {
            int c = skipWhileSpace();
            long sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = next();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble() {
            return Double.valueOf(nextToken());
        }

        int skipWhileSpace() {
            int c = next();
            while (isSpaceChar(c)) {
                c = next();
            }
            return c;
        }

        boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    }
}