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())


res = 0
ip = pow(p-1,p-2,p)
for i in range(1,p):
    n = (b * pow(pow(a,i,p),p-2,p))%p
    u = (n - i + p )%p
    u = (u * ip)%p
    me = u * (p-1) + i
    if me>x: continue
    res+= (x-me) // (p*(p-1))+1

print(res)


# (u*(p-1) + i) * a^i = b mod p
# u*(p-1) + i = b * inv (a^i) % mod p