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 = map(int, input().split())
ans = 0
ainv = 1
for i in range(p - 2):
    ainv = (ainv * a) % p
rem = 1
inv = 1
lcm = p * (p - 1)
for n in range(1, p):
    rem = (rem * a) % p
    inv = (inv * ainv) % p
    i0 = min(p, ((n * rem - b) * inv + p) % p)
    n0 = n + i0 * (p - 1)
    ans += max(0, (x - n0 + lcm) // lcm)
print(ans)