82 - ZOJ Monthly, August 2009 - G
Smallchen's major is Information Science & Electronic Engineering, so he often needs to deal with signals. To simplify the problem, we regard signals as functions of time.
Smallchen is analysing a kind of signal these days. Its formula is f(t) = an * tn + ... + a1 * t. He knows the time when each top peak or bottom peak shows up, and he wants to know the first non-zero number after the decimal point of each ai (i from 1 to n).
To make the coefficients unique, we add a constraint that an * n = 1
The first line of the input contains an integer T (1 <= T <= 10000), indicating the number of test cases.
For each case, the first line contains an integer n (2 <= n <= 32) as mentioned before. The second line contains n - 1 distinct integers Ti (1 <= Ti <= 10000), which means f(-Ti) is a top peak or bottom peak. Top peaks or bottom peaks mean that f(t) gets maximal or minimal at that small period of time around -Ti. Remember that it's -Ti instead of Ti.
For each case, output the first non-zero number after decimal point of each ai (i from 1 to n) in one line separated by a space(no extra space at the end of each line). If ai is an integer, then output a zero.
2 2 1 3 1 2
0 5 0 5 3
Author: CHEN, Shimou