Safety in Numbers (Small)

A reality TV show has $N$ contestants. The judges give contestant $i$ an integer score $s_i$. The audience then splits its vote among the contestants: contestant $i$ takes a fraction $y_i$ of the audience vote, every $y_i$ is between 0 and 1 inclusive, and $y_0 + y_1 + \dots + y_{N-1} = 1$.

Let $X = s_0 + s_1 + \dots + s_{N-1}$. The final score of contestant $i$ is $s_i + X y_i$.

The contestant with the lowest final score is eliminated. If two or more contestants tie for the lowest final score, nobody is eliminated.

Contestant $i$ is safe at a given $y_i$ when no way of splitting the remaining $1 - y_i$ of the audience vote among the other contestants eliminates contestant $i$. For each contestant, find the smallest $y_i$ that makes the contestant safe, written as a percentage.

The first line has one integer $T$, the number of test cases. Each of the next $T$ lines holds one test case: the number of contestants $N$, then $N$ integers $s_0, s_1, \dots, s_{N-1}$, all separated by single spaces. The integer $s_i$ is the score the judges gave contestant $i$.

Limits

• $1 \le T \le 20$
• $2 \le N \le 10$
• $0 \le s_i \le 100$
• $s_i > 0$ for at least one $i$, so $X > 0$.

For each test case print one line: Case #x: followed by $N$ numbers $m_0, m_1, \dots, m_{N-1}$ separated by single spaces. Here $x$ is the case number starting from 1, and $m_i$ is the smallest percentage of the audience vote that makes contestant $i$ safe.

Print each $m_i$ with exactly six digits after the decimal point, rounding a value that lands exactly halfway upward. Every $m_i$ is a rational number, and no test case has an answer sitting on a rounding boundary, so ordinary fixed-point printing of a correctly computed answer matches.