 He is Flying

Problem Description
JRY wants to drag racing along a long road. There are n sections on the road, the ith section has a nonnegative integer length si. JRY will choose some continuous sections to race (at an unbelievable speed), so there are totally n(n+1)2 different ways for him to ride. If JRY rides across from the ith section to the jth section, he would gain j−i+1 pleasure. Now JRY wants to know, if he tries all the ways whose length is s, what's the total pleasure he can get. Please be aware that in the problem, the length of one section could be zero, which means that the length is so trivial that we can regard it as 0.Input
The first line of the input is a single integer T (T=5), indicating the number of testcases.For each testcase, the first line contains one integer n. The second line contains n nonnegative integers, which mean the length of every section. If we denote the total length of all the sections as s, we can guarantee that 0≤s≤50000 and 1≤n≤100000.
Output
For each testcase, print s+1 lines. The single number in the ith line indicates the total pleasure JRY can get if he races all the ways of length i−1.Sample Input
2
3
1 2 3
4
0 1 2 3Sample Output
0
1
1
3
0
2
3
1
3
1
6
0
2
7