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:
import sys

def calc(a, b, p, x):
    ans = 0
    power = pow(a, p - 2, p)
    a2, b2, s, d1 = 1, b, 0, -b
    prod = p * (p - 1)
    while s < p - 1:
        k = (d1 + s) % p
        L = x - s - (p - 1) * k
        ans += L // prod + 1
        d1 = (d1 * power) % p
        s += 1
    return str(ans)
 
 
a, b, p, x = list(map(int,sys.stdin.readline().split()))
sys.stdout.write(calc(a, b, p, x))