CF1409B.Minimum Product

普及/提高-

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题目描述

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.

输入格式

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.

输出格式

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.

输入输出样例

输入#1

7
10 10 8 5 3
12 8 8 7 2
12343 43 4543 39 123212
1000000000 1000000000 1 1 1
1000000000 1000000000 1 1 1000000000
10 11 2 1 5
10 11 9 1 10

输出#1

70
77
177177
999999999000000000
999999999
55
10

说明/提示

In the first test case of the example, you need to decrease $b$ three times and obtain $10 \cdot 7 = 70$ .

In the second test case of the example, you need to decrease $a$ one time, $b$ one time and obtain $11 \cdot 7 = 77$ .

In the sixth test case of the example, you need to decrease $a$ five times and obtain $5 \cdot 11 = 55$ .

In the seventh test case of the example, you need to decrease $b$ ten times and obtain $10 \cdot 1 = 10$ .

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