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:
a, b, p, x = map(int, raw_input().strip().split())
a = pow(a, p - 2, p)

d = {}
for r in xrange(p - 1):
    s = b * pow(a, r, p) % p
    res = (s + ((r - s) % (p - 1)) * p) % (p * (p - 1))

    try: d[res] += 1
    except: d[res] = 1

ans = 0
Q = x // (p * (p - 1))
R = x % (p * (p - 1))

for r in d:
    if r <= R: ans += (Q + 1)
    else: ans += Q

print ans