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=[int(k) for k in raw_input().split(" ")]


res=0
mp=range(p)
ma=[0 for k in range(p-1)]
ppm1=p*(p-1)
for i in range(0,p-1):
    ma[i]=(ma[i-1]*a)%p if i else 1
##Oooh, si n%p=ma[p-1-n%p-1] c bon!
    #Candidat
    mp=(ma[i]*b)%p
    mpm1=(-i)%(p-1)
    mppm1=((mpm1-mp)*(p-1)+mpm1)%ppm1
    #print mp,mpm1,mppm1
    if mppm1<=x:
        res+=(x-mppm1)/ppm1 +1
print res