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 egcd(a, b):
    if b == 0:
        return 1, 0, a
    x1, y1, c = egcd(b, a % b)
    return y1, x1 - (a / b) * y1, c

def crt(a0, n0, a1, n1):
    if min(n0, n1) < 0:
        return 0, -1
    x, y, g = egcd(n0, n1)
    if (a0 - a1) % g:
        return 0, -1
    x *= (a1 - a0) / g
    y *= (a1 - a0) / g
    k = n1 * n0 / g
    return (n0 * x + a0) % k, k

a, b, p, x = map(int, raw_input().split())
inv = [1] * p
for i in range(2, p):
    q = p / i
    r = p % i
    inv[i] = p - inv[r] * q % p

ans = 0
ai = 1
for i in range(p - 1):
    a1 = inv[ai] * b
    a0, n0 = crt(a1, p, i, p - 1)
    if x >= a0:
        ans += 1 + (x - a0) / n0
    ai = ai * a % p
print(ans)