Last eight digits of a power tower

For positive integers $a$ and $b$, write the $b$-th power tower of $a$ as $a \uparrow\uparrow b$. It is defined by

$a \uparrow\uparrow 1 = a$

$a \uparrow\uparrow (k + 1) = a^{(a \uparrow\uparrow k)}$

For example, $3 \uparrow\uparrow 2 = 3^3 = 27$ and $3 \uparrow\uparrow 3 = 3^{27} = 7625597484987$.

Find the last 8 digits of $a \uparrow\uparrow b$.

The first line contains two positive integers $a$ and $b$, separated by a space. ($1 \le a, b \le 20000$)

Print the last 8 digits of $a \uparrow\uparrow b$ on one line.

If $a \uparrow\uparrow b$ has 9 or more digits, print those last 8 digits exactly, including any zeros at the front of them. If $a \uparrow\uparrow b$ has 8 or fewer digits, print the whole value without adding leading zeros.