B. Monsters
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Monocarp is playing yet another computer game. And yet again, his character is killing some monsters. There are $$$n$$$ monsters, numbered from $$$1$$$ to $$$n$$$, and the $$$i$$$-th of them has $$$a_i$$$ health points initially.

Monocarp's character has an ability that deals $$$k$$$ damage to the monster with the highest current health. If there are several of them, the one with the smaller index is chosen. If a monster's health becomes less than or equal to $$$0$$$ after Monocarp uses his ability, then it dies.

Monocarp uses his ability until all monsters die. Your task is to determine the order in which monsters will die.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

The first line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 3 \cdot 10^5$$$; $$$1 \le k \le 10^9$$$) — the number of monsters and the damage which Monocarp's ability deals.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$) — the initial health points of monsters.

The sum of $$$n$$$ over all test cases doesn't exceed $$$3 \cdot 10^5$$$.

Output

For each test case, print $$$n$$$ integers — the indices of monsters in the order they die.

Example
Input
3
3 2
1 2 3
2 3
1 1
4 3
2 8 3 5
Output
2 1 3 
1 2 
3 1 2 4
Note

In the first example, the health points change as follows: $$$[1, 2, \underline{3}] \rightarrow [1, \underline{2}, 1] \rightarrow [\underline{1}, 0, 1] \rightarrow [-1, 0, \underline{1}] \rightarrow [-1, 0, -1]$$$. The monster that is going to take damage the next time Monocarp uses his ability is underlined.

In the second example, the health points change as follows: $$$[\underline{1}, 1] \rightarrow [-2, \underline{1}] \rightarrow [-2, -2]$$$.

In the third example, the health points change as follows: $$$[2, \underline{8}, 3, 5] \rightarrow [2, \underline{5}, 3, 5] \rightarrow [2, 2, 3, \underline{5}] \rightarrow [2, 2, \underline{3}, 2] \rightarrow [\underline{2}, 2, 0, 2] \rightarrow [-1, \underline{2}, 0, 2] \rightarrow [-1, -1, 0, \underline{2}] \rightarrow [-1, -1, 0, -1]$$$.