Given a sequence of n integers called W and an integer m. For each i (1 <= i <= n), you can choose some elements Wk (1 <= k < i), and change them to zero to make ∑i j=1 Wj<=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 <= Wi<= m
Output
For each test case, you should output n integers in one line: i-th integer means the minimum number of chosen elements Wk (1 <= k < i), and change them to zero to make ∑i j=1 Wj<=m.