Problem Description

Given a sequence of n integers called W and an integer m. For each i (1 <= i <= n), you can choose some elements $W_k$ (1 <= k < i), and change them to zero to make $\sum_{j=1}^i$$W_j$<=m. So what's the minimum number of chosen elements to meet the requirements above?.

Input

The first line contains an integer Q --- the number of test cases.
For each test case:
The first line contains two integers n and m --- n represents the number of elemens in sequence W and m is as described above.
The second line contains n integers, which means the sequence W.

1 <= Q <= 15
1 <= n <= 2*$10^5$
1 <= m <= $10^9$
For each i, 1 <= $W_i$ <= m

Output

For each test case, you should output n integers in one line: i-th integer means the minimum number of chosen elements $W_k$ (1 <= k < i), and change them to zero to make $\sum_{j=1}^i$$W_j$<=m.

2  
7 15  
1 2 3 4 5 6 7  
5 100  
80 40 40 40 60

0 0 0 0 0 2 3  
0 1 1 2 3