Problem 1. Chip Exchange

USACO 2026 First Contest, Bronze

Bessie the cow has in her possession $A$ chips of type A and $B$ chips of type B ($0\le A,B\le 10^9$). She can perform the following operation as many times as she likes:

• If you have at least $c_B$ chips of type B, exchange $c_B$ chips of type B for $c_A$ chips of type A ($1\le c_A,c_B\le 10^9$).

Determine the minimum non-negative integer $x$ such that the following holds: after receiving $x$ additional random chips, it is guaranteed that Bessie can end up with at least $f_A$ chips of type A ($0\le f_A\le 10^9$).

INPUT FORMAT (input arrives from the terminal / stdin):

The first line contains $T$, the number of independent test cases ($1\le T\le 10^4$).

Then follow $T$ tests, each consisting of five integers $A,B,c_A,c_B,f_A$.

OUTPUT FORMAT (print output to the terminal / stdout):

Output the answer for each test on a separate line.

Note: The large size of integers involved in this problem may require the use of 64-bit integer data types (e.g., a "long long" in C/C++).

SAMPLE INPUT:

2
2 3 1 1 6
2 3 1 1 4

SAMPLE OUTPUT:

1
0

SAMPLE INPUT:

5
0 0 2 3 5
0 1 2 3 5
1 0 2 3 5
10 10 2 3 5
0 0 1 1000000000 1000000000

SAMPLE OUTPUT:

9
8
7
0
1000000000000000000

For the first test, Bessie initially starts with no chips. If she receives any $9$ additional chips, she can perform the operation to end up with at least $5$ chips of type A. For example, if she receives $2$ chips of type A and $7$ chips of type B, she can perform the operation twice to end up with $6\ge 5$ chips of type A. However, if she only receive $8$ chips of type B, she can only end up with $4<5$ chips of type A.

For the fourth test, she already has enough chips of type A from the start.

SCORING: Input 3: $c_A=c_B=1$Inputs 4-5: $x\le 10$ for all casesInputs 6-7: $c_A=2$, $c_B=3$Inputs 8-12: No additional constraints.

Problem credits: Benjamin Qi