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 = [int(x) for x in input().split()]

ainv = pow(a,p-2,p)

count = 0

n = 1
exp = ainv*b%p
while n<p:
    m = n
    if exp>n:
        m += (n+p-exp)*(p-1)
    else:
        m += (n-exp)*(p-1)
    
    if m<=x: count += 1 + (x-m)//(p*(p-1))
    
    n += 1
    exp = (exp*ainv)%p

print(count)