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:
from fractions import gcd
from math import factorial, ceil, sqrt, atan2, log, pi, e
from itertools import *
import string
import copy
import random
import bisect
from decimal import *
def id_generator(size=20, chars=string.digits):
    return ''.join(random.choice(chars) for _ in range(size))
 
def mp():
    return map(int,str(raw_input()).split())

a,b,p,x=mp()
ans=0
inv_mod=pow(a,p-2,p)
d=-b
bla=p*(p-1)

for i in range(p-1):
	val=(d+i)%p
	val*=(p-1)
	val=x-i-val
	ans+=val/bla+1
	d*=inv_mod
	d%=p

print ans