B. Minimum Producttime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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.OutputFor 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.ExampleInput
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
Output
70
77
177177
999999999000000000
999999999
55
10
NoteIn 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.
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

70 77 177177 999999999000000000 999999999 55 10 
['brute force', 'greedy', 'math', '*1100']