Balloon Distribution

A contest has $M$ contestants. Contestant $i$ scored $P_i$ points, for $i = 1, 2, \dots, M$.

The organizers have $N$ balloons and hand them out by the following rule.

1. For every contestant $i$ and every positive integer $j = 1, 2, 3, \dots$, compute the ratio $P_i / j$.
2. Collect all of these ratios into one list and rank them from the largest value down to the smallest. Equal ratios share the same rank: the rank of a ratio is one plus the number of ratios strictly larger than it.
3. A contestant receives one balloon for each of their own ratios whose rank is at most $N$. When several ratios tie at the last rank that still earns a balloon, every ratio tied there earns one, so the number of balloons handed out can be larger than $N$.

Report how many balloons each contestant receives.

For example, take $M = 5$ contestants with $P_1 = 274771$, $P_2 = 344854$, $P_3 = 773780$, $P_4 = 627629$, $P_5 = 386890$, and $N = 10$ balloons. The ratios, rounded to two decimals, start like this.

Their ranks are below. A rank in bold is at most $N = 10$, so that ratio earns a balloon. Every ratio with $j \ge 6$ has a rank greater than 10 here.

The five contestants therefore receive 1, 1, 4, 3, and 2 balloons. That is 11 balloons in total, because $773780 / 4$ and $386890 / 2$ are both equal to $193445$ and tie at rank 10.

The first line contains $T$, the number of test cases.

Each test case takes two lines. The first line contains two integers $M$ and $N$ separated by a space. The second line contains $M$ space separated integers $P_1, P_2, \dots, P_M$.

Constraints:

• $1 \le T \le 3000$
• $1 \le M \le 10^5$
• the sum of $M$ over all test cases is at most $4 \times 10^5$
• $1 \le N \le 10^9$
• $1 \le P_i \le 10^9$

For each test case, print one line with $M$ integers separated by single spaces. The $i$-th integer is the number of balloons contestant $i$ receives.