BERNULLI  Bernoulli numbers
Your task is to compute natural logarithm of the absolute value of the Bernoulli number for many integer parameters N.
I/O format is the same as in BINARYIO.
Input
Array of unsigned 32 bit integers in binary format (use fread in C/C++)
To read unsigned N use fread(&N, sizeof(N), 1, stdin) instead of usual scanf("%u", &N) until the end of file.
For each test case 2 ≤ N < 2^{32}, N is even. There will be up to 1,250,000 numbers in input file.
Output
Array of doubles in binary format (use fwrite in C/C++)
To write double a use fwrite(&a, sizeof(a), 1, stdout) instead of usual printf("%lf\n", a).
For each N output ln(B_{N}) with absolute or relative error less than 10^{15}
Example
Input:
4
10
50
Output:
3,4011973816621553754132366916069
2,580216829592325170273661603119
57,277060811865704087099873424857
Sample input and output are readable for your convenience!!!
TL = 5 * My time
hide comments
taranov_srg:
20201215 22:34:57
@mikhaelkh is the idea of using the Bernouli_N approximation by 2*N!/(2*Pi)^N starting any N correct? 

Krystian Plackowski:
20181101 01:11:36
I will leave a hint for followers: Bernoulli numbers, that are less than 1 produce the biggest error... and there are not too many of them. Last edit: 20181101 19:57:39 

Francky:
20170214 20:14:57
judge => http://www.spoj.com/files/judge/12890/

Added by:  Michael Kharitonov 
Date:  20170214 
Time limit:  0.200s 
Source limit:  10000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  CCLANG C C++ 4.3.2 CPP CPP14 CPP14CLANG C99 