Function

You are given a function $f \\, : \\, \mathbb{N}\_0 \to \mathbb{N}\_0$ defined as below. ($\mathbb{N}\_0$ denotes the set of non-negative integers.)

• $f(0) = a\_0$
• $f(i) = a\_i^{f(i - 1)}$ ($i \ge 1$)

Find the value of $f(n)$ modulo $m$.

The first line contains a single integer $n$.

The second line contains $n + 1$ integers $a\_0, \\, a\_1, \\, \cdots, \\, a\_n$.

The third line contains a single integer $m$.

Print the value of $f(n)$ modulo $m$.

• $0 \le n \le 2$
• $1 \le a\_i \le 2 \times 10^9$ ($0 \le i \le n$)
• $2 \le m < 2 \times 10^9$; $m$ is a prime number.
• All values in input are integers.

As a note, the exact value of $9^{9^9}$ has a whopping $369 \\, 693 \\, 700$ digits.