Given an integer $x$. Your task is to find out how many positive integers $n$ ($1 \leq n \leq x$) satisfy \[n \cdot a^n \equiv b \quad (\textrm{mod}\;p),\] where $a, b, p$ are all known constants.

-----Input-----

The only line contains four integers $a,b,p,x$ ($2 \leq p \leq 10^6+3$, $1 \leq a,b < p$, $1 \leq x \leq 10^{12}$). 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.