Problem: Given an integer x. Your task is to find out how many positive integers n (1 ≤ n ≤ x) satisfy $$$n ⋅ a^n ≡ b   (mod\;p), where a, b, p$$$ are all known constants.

Input

The only line contains four integers a,b,p,x (2 ≤ p ≤ 10^6+3, 1 ≤ a,b < p, 1 ≤ x ≤ 10^{12}). It is guaranteed that p is a prime.

Output

Print a single integer: the number of possible answers n.

Examples

Input

2 3 5 8


Output

2


Input

4 6 7 13


Output

1


Input

233 233 10007 1


Output

1

Note

In the first sample, we can see that n=2 and n=8 are possible answers.

Solution (in PYTHON3):

Solution:
a, b, p, x = [int(x) for x in input().split()]

powers = [a]

while powers[-1] != 1:
    powers.append(powers[-1] * a % p)
    
order = len(powers)
powers = [powers[-1]] + powers

inverse = pow(order, p-2, p)

def f(sol):
    return (x // (p * order)) + (1 if sol <= x % (p * order) else 0)

def chinese(a, n, b, m):
    k = inverse * (b - a + m) % m
    x = k * n + a
    return x % (n * m)

res = 0
for i in range(len(powers)-1):
    inv = powers[order - i]
    val = inv * b % p
    
    sol = chinese(i, order, val, p)
    
    res += f(sol)
    
print(res)