E. Equalising Audio
time limit per test
4 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

As 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.

Input

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

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 $$$10^{-6}$$$.

Examples
Input
5 6
0 1 -2 3 -4
Output
0 1 -2 3 -4
Input
4 1
1 3 3 7
Output
0.242535625 0.7276068751 0.7276068751 1.697749375