CF1849B.Monsters

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题目描述

Monocarp is playing yet another computer game. And yet again, his character is killing some monsters. There are nn monsters, numbered from 11 to nn, and the ii-th of them has aia_i health points initially.

Monocarp's character has an ability that deals kk 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 00 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.

莫诺卡普正在玩另一款电脑游戏。同样地,他的角色正在击杀一些怪物。共有 nn 只怪物,编号从 11 到 nn,其中第 ii 只怪物的初始生命值为 aia_i。

莫诺卡普的角色拥有一种技能,该技能会对当前生命值最高的怪物造成 kk 点伤害。若存在多个生命值最高的怪物,则选择编号最小的那个。若莫诺卡普使用该技能后某只怪物的生命值降至 00 或更低,则该怪物死亡。

莫诺卡普将持续使用该技能,直至所有怪物均死亡。你的任务是确定怪物死亡的顺序。

输入格式

The first line contains a single integer tt (1≤t≤1041 \le t \le 10^4) — the number of test cases.

The first line of each test case contains two integers nn and kk (1≤n≤3⋅1051 \le n \le 3 \cdot 10^5; 1≤k≤1091 \le k \le 10^9) — the number of monsters and the damage which Monocarp's ability deals.

The second line contains nn integers a1,a2,…,ana_1, a_2, \dots, a_n (1≤ai≤1091 \le a_i \le 10^9) — the initial health points of monsters.

The sum of nn over all test cases doesn't exceed 3⋅1053 \cdot 10^5.

第一行包含一个整数 tt(1≤t≤1041 \le t \le 10^4)—— 测试用例的数量。

每个测试用例的第一行包含两个整数 nn 和 kk(1≤n≤3⋅1051 \le n \le 3 \cdot 10^5;1≤k≤1091 \le k \le 10^9)—— 怪物的数量以及 Monocarp 技能造成的伤害值。

每个测试用例的第二行包含 nn 个整数 a1,a2,…,ana_1, a_2, \dots, a_n(1≤ai≤1091 \le a_i \le 10^9)—— 各怪物的初始生命值。

所有测试用例中 nn 的总和不超过 3⋅1053 \cdot 10^5。

输出格式

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

对于每个测试用例,输出 nn 个整数——即怪物死亡顺序的索引。

输入输出样例

  • 输入#1

    3
    3 2
    1 2 3
    2 3
    1 1
    4 3
    2 8 3 5

    输出#1

    2 1 3 
    1 2 
    3 1 2 4

说明/提示

In the first example, the health points change as follows: [1,2,3‾]→[1,2‾,1]→[1‾,0,1]→[−1,0,1‾]→[−1,0,−1][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: [1‾,1]→[−2,1‾]→[−2,−2][\underline{1}, 1] \rightarrow [-2, \underline{1}] \rightarrow [-2, -2].

In the third example, the health points change as follows: [2,8‾,3,5]→[2,5‾,3,5]→[2,2,3,5‾]→[2,2,3‾,2]→[2‾,2,0,2]→[−1,2‾,0,2]→[−1,−1,0,2‾]→[−1,−1,0,−1][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].

在第一个例子中,生命值的变化过程如下:[1,2,3‾]→[1,2‾,1]→[1‾,0,1]→[−1,0,1‾]→[−1,0,−1][1, 2, \underline{3}] \rightarrow [1, \underline{2}, 1] \rightarrow [\underline{1}, 0, 1] \rightarrow [-1, 0, \underline{1}] \rightarrow [-1, 0, -1]。每次 Monocarp 使用技能时,即将受到伤害的怪物用下划线标出。

在第二个例子中,生命值的变化过程如下:[1‾,1]→[−2,1‾]→[−2,−2][\underline{1}, 1] \rightarrow [-2, \underline{1}] \rightarrow [-2, -2]。

在第三个例子中,生命值的变化过程如下:[2,8‾,3,5]→[2,5‾,3,5]→[2,2,3,5‾]→[2,2,3‾,2]→[2‾,2,0,2]→[−1,2‾,0,2]→[−1,−1,0,2‾]→[−1,−1,0,−1][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]。

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