A13692 | Minimum Product

You are given four integers $a$ , $b$ , $x$ and $y$ . Initially, $a \ge x$ and $b \ge y$ . You can do the following operation no more than $n$ times:

- Choose either $a$ or $b$ and decrease it by one. However, as a result of this operation, value of $a$ cannot become less than $x$ , and value of $b$ cannot become less than $y$ .

Your task is to find the minimum possible product of $a$ and $b$ ( $a \cdot b$ ) you can achieve by applying the given operation no more than $n$ times.

You have to answer $t$ independent test cases.

The first line of the input contains one integer $t$ ( $1 \le t \le 2 \cdot 10^4$ ) — the number of test cases. Then $t$ test cases follow.

The only line of the test case contains five integers $a$ , $b$ , $x$ , $y$ and $n$ ( $1 \le a, b, x, y, n \le 10^9$ ). Additional constraint on the input: $a \ge x$ and $b \ge y$ always holds.

For each test case, print one integer: the minimum possible product of $a$ and $b$ ( $a \cdot b$ ) you can achieve by applying the given operation no more than $n$ times.