Super Knight

Hyeonjeong plays a chess variant with its own rules. The board has $N$ rows and $M$ columns, and the super knight is the only piece she can use.

From the square it stands on, the super knight moves to a square offset by $(+a, +b)$, $(+a, -b)$, $(-a, +b)$, $(-a, -b)$, $(+b, +a)$, $(+b, -a)$, $(-b, +a)$, $(-b, -a)$. An ordinary chess knight is the case $a = 2$ and $b = 1$.

There are 8 candidate moves in total, but the knight cannot move to a destination that lies outside the board.

Given $a$, $b$, $N$, $M$, and $k$, write a program that counts the squares of the board from which exactly $k$ moves are possible.

The first line contains $a$, $b$, $N$, $M$, and $k$, separated by spaces. ($1 \le a, b, N, M \le 10^9$, $a \ne b$, $2 \times \max(a, b) < \min(N, M)$, $0 \le k \le 8$)

Print the number of squares from which exactly $k$ moves are possible.