Countdown

The TV show Countdown has a round where you obtain a number by combining six different numbers using the four basic operations: addition, subtraction, multiplication, and division. The basic rules are:

• The contestant selects six of twenty-four shuffled tiles. The tiles form two groups: four "large numbers" ($25, 50, 75, 100$) and the rest "small numbers", which are two copies each of $1$ through $10$. So the tile values come from $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 25, 50, 75, 100\}$.
• The contestant chooses how many large numbers are in the selection, anywhere from none.
• The contestant then has thirty seconds to get a number as close to the target as possible by combining the six selected numbers using addition, subtraction, multiplication, and division.
• Not all numbers need to be used.
• A number can be used as many times as it appears.
• Fractions are not allowed; only positive integers may appear at any stage of the calculation.

Given the six numbers and a target $T$, determine how close to $T$ you can get.

The first line contains the number of cases $C$ ($1 \le C \le 50$). Each of the following $C$ lines contains six natural numbers from the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 25, 50, 75, 100\}$ followed by a natural number $T$ ($1 \le T \le 999$), the target.

For each case, print on its own line a single integer: the smallest possible value of $|v - T|$ over all numbers $v$ obtainable from the six selected numbers under the rules above. Every selected number by itself counts as obtainable, so this value is always defined; it is $0$ exactly when the target itself can be reached.