
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) = a_{n} * t^{n} + ... + a_{1} * t. He knows the time when each top peak or bottom peak shows up, and he wants to know the first nonzero number after the decimal point of each a_{i} (i from 1 to n). To make the coefficients unique, we add a constraint that a_{n} * n = 1 Input 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 T_{i} (1 <= T_{i} <= 10000), which means f(T_{i}) 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 T_{i}. Remember that it's T_{i} instead of T_{i}. Output For each case, output the first nonzero number after decimal point of each a_{i} (i from 1 to n) in one line separated by a space(no extra space at the end of each line). If a_{i} is an integer, then output a zero. Sample Input 2 2 1 3 1 2 Sample Output 0 5 0 5 3 Author: CHEN, Shimou 