레이팅 미적용As a radio engineer at the Balanced Audio Podcast your job is to deliver an equal listening experience at all times. You did a poll among the listeners and they are especially concerned about fluctuations in loudness. To resolve this you bought a transformer to equalise the audio, but alas, its software got corrupted during transport.
Your job is to rewrite the equalising software. As input the transformer gets \(n\) amplitudes \(a_1, \ldots, a_n\), with an average perceived loudness of \(\frac{1}{n}\sum_{i=1}^n a_i^2\). The output should contain the same amplitudes, but renormalised by some constant positive factor, such that the average perceived loudness is \(x\). There is one exception: total silence should always be preserved.
The input consists of:
- One line with a two integers \(n\) and \(x\) (\(1\leq n\leq 10^5\), \(0 \leq x \leq 10^6)\), the number of amplitudes and the average perceived loudness to achieve.
- One line with \(n\) integers \(a_1, \ldots, a_n\) (\(\left| a_i \right| \leq 10^6\)), the amplitudes.
Output one line containing \(n\) numbers, the renormalised amplitudes with an average perceived loudness of \(x\).
Your answers should have an absolute or relative error of at most \(10^{-6}\).
5 6
0 1 -2 3 -4
0 1 -2 3 -4
4 1
1 3 3 7
0.242535625 0.7276068751 0.7276068751 1.697749375