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 PYTHON):

Solution:
def phi(x):
    res = x
    y = x
    for i in xrange(2, 1010):
        if y % i == 0:
            res = res / i * (i - 1)
            while y % i == 0:
                y /= i
    if y > 1:
        res = res / y * (y - 1)
    return res
def main():
    a, b, p, x = map(int, raw_input().split())
    if a == 1:
        q, r = divmod(x, p)
        print q + (b <= r)
        return
    a = pow(a, p - 2, p)
    t = b
    f = p * (p - 1)
    q, r = divmod(x, f)
    pp = pow(p - 1, p - 2, p) * (p - 1)
    ph = pow(p, phi(p - 1) - 1, p - 1) * p
    ans = (p - 1) * q
    if not r:
        print ans
        return
    for i in xrange(p - 1):
        s = (i * ph + t * pp) % f
        if s <= r:
            ans += 1
        t = t * a % p 
    print ans
main()