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 PYTHON3):

Solution:
from collections import defaultdict

class Combinatorics:
    def __init__(self, N, mod):
        '''
        Preprocess for calculating binomial coefficients nCr (0 <= r <= n, 0 <= n <= N)
        over the finite field Z/(mod)Z.
        Input:
            N (int): maximum n
            mod (int): a prime number. The order of the field Z/(mod)Z over which nCr is calculated.
        '''
        self.mod = mod
        self.fact = {i: None for i in range(N+1)}         # n!
        self.inverse = {i: None for i in range(1, N+1)}   # inverse of n in the field Z/(MOD)Z
        self.fact_inverse = {i: None for i in range(N+1)} # inverse of n! in the field Z/(MOD)Z
        
        # preprocess
        self.fact[0] = self.fact[1] = 1
        self.fact_inverse[0] = self.fact_inverse[1] = 1
        self.inverse[1] = 1
        for i in range(2, N+1):
            self.fact[i] = i * self.fact[i-1] % self.mod
            q, r = divmod(self.mod, i)
            self.inverse[i] = (- (q % self.mod) * self.inverse[r]) % self.mod
            self.fact_inverse[i] = self.inverse[i] * self.fact_inverse[i-1] % self.mod
    
    def binom(self, n, r):
        '''
        Calculate nCr = n! /(r! (n-r)!) % mod
        '''
        if n < r or n < 0 or r < 0:
            return 0
        else:
            return self.fact[n] * (self.fact_inverse[r] * self.fact_inverse[n-r] % self.mod) % self.mod

N, M = map(int, input().split())
com = Combinatorics(N, M)
ans = 0

# Preprocess
# calculate 2**n and 2**(2**n)
pow2 = [0] * (N*N // 4 + 1)
pow_pow2 = [0] * (N+1)
pow2[0] = 1; pow_pow2[0] = 2
for i in range(1, N*N // 4 + 1):
    pow2[i] = (pow2[i-1] * 2) % M
for i in range(1, N+1):
    pow_pow2[i] = pow(pow_pow2[i-1], 2, M)

# (#ways to order i ramens, with each of n toppings chosen at most once)
ways2 = {n: defaultdict(int) for n in range(N+1)}
for n in range(N+1):
    ways = 0 # (#ways to choose n toppings, with each topping chosen at most once)
    temp = 0
    if n >= 1:
        for i in range(n+1):
            ways2[n][i] = (ways2[n][i] +  ways2[n-1][i]) % M # n-th topping is not used
            if i >= 1: ways2[n][i] = (ways2[n][i] + ways2[n-1][i-1]) % M # only n-th topping is used in an order
            ways2[n][i] = (ways2[n][i] + (i*ways2[n-1][i]) % M) % M # n-th topping is chosen with another topping
            temp = (temp + (ways2[n][i] * pow2[(N-n)*i]) % M) % M # degree of freedom on each order is 2**(N-n)
    else: # n = 0
        ways2[n][0] = 1
        temp += ways2[n][0]
    ways = (temp * pow_pow2[N-n]) % M
    if n % 2 == 0:
        ans = (ans + (com.binom(N, n) * ways) % M) % M
    else:
        ans = (ans - (com.binom(N, n) * ways) % M) % M
print(ans)