Equalising Audio

문제

As a radio engineer at the Balanced Audio Podcast \copyright{} 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 $nn$ amplitudes $a_1,\dots ,a_{n}a\_1,\; \backslash ldots,\; a\_n$, with an average perceived loudness of $\frac{1}{n}{\sum }_{i=1}^n{a}_i^2\backslash frac\{1\}\{n\}\backslash sum\_\{i=1\}^n\; a\_i^2$. The output should contain the same amplitudes, but renormalised by some constant positive factor, such that the average perceived loudness is $xx$. There is one exception: total silence should always be preserved.

입력

The input consists of:

• One line with a two integers $nn$ and $xx$ ($1\le n\le {10}^{5}1\backslash leq\; n\backslash leq\; 10^5$, $0\le x\le {10}^6)0\; \backslash leq\; x\; \backslash leq\; 10^6)$, the number of amplitudes and the average perceived loudness to achieve.
• One line with $nn$ integers $a_1,\dots ,a_{n}a\_1,\; \backslash ldots,\; a\_n$ ($\mid a_i\mid \le {10}^6\backslash left|\; a\_i\; \backslash right|\; \backslash leq\; 10^6$), the amplitudes.

출력

Output one line containing $nn$ numbers, the renormalised amplitudes with an average perceived loudness of $xx$.

Your answers should have an absolute or relative error of at most ${10}^{-6}10^\{-6\}$.