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 = list(map(int, input().strip().split()))


def brute(a,b,p,x):
    for n in range(1, x+1):
        if (n*pow(a,n,p)) % p == b:
            print(n)

#brute(a,b,p,x)

sols = 0

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

##print('a', inva)

a2 = 1
b2 = b
s = 0
d1 = -b
fac = p*(p-1)
while s < p-1:
    k = (d1 + s) % p
    u = k
    L = x - s - (p-1)*k
    sols += L//fac + 1
##    while (p-1)*u + s <= x:
##        n = (p-1)*u + s
##        print(s, k, n)
##        print(n)
##        #print(n*pow(a,n,p) % p, b)
##        sols += 1
##        u += p
    d1 = (d1 * inva) % p
    s += 1

print(sols)