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ZOJ Problem Set - 3237
Signals and Systems

Time Limit: 4 Seconds      Memory Limit: 32768 KB

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

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 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.

Output

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.

Sample Input

2
2
1
3
1 2

Sample Output

0 5
0 5 3

Author: CHEN, Shimou
Source: ZOJ Monthly, August 2009
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