CF1409B 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.

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 $ .