[Solution] Infernos solution codechef

Infernos solution codechef – Ved started playing a new mobile game called Fighting Clans. An army of N enemies is approaching his base. The ith enemy has Hi health points. An enemy gets killed if his health points become 0.

[Solution] Infernos solution codechef

Ved defends his base using a weapon named Inferno. He can set the Inferno to one of the following two modes:

Single-Target Mode: In one second, the Inferno can target exactly one living enemy and cause damage of at most X health points.
Multi-Target Mode: In one second, the Inferno can target all living enemies and cause damage of 1 health point to each of them.

Find the minimum time required to kill all the enemies.

Note: Ved is not allowed to change the mode of the weapon once it is set initially.

Input Format

The first line contains a single integer T – the number of test cases. Then the test cases follow.

The first line of each test case contains two integers N and X – the number of enemies and the damage caused by the single-target mode of Inferno in one second respectively.

The second line of each test case contains N space-separated integers H1,H2,…,HN where Hi denotes the initial health points of ith enemy.

[Solution] Infernos solution codechef

For each test case, output in a single line, the minimum time required to kill all the enemies.

Constraints

  • 1≤T≤1000
  • 1≤N≤200
  • 1≤X≤100
  • 1≤Ai≤100

Sample Input 1

4
5 4
2 2 4 1 1
3 5
5 4 5
4 4
4 4 4 4
3 10
7 8 9

[Solution] Infernos solution codechef

4
3
4
3

Explanation

Test case 1: In single-target mode, all enemies can be killed in 1 second each. Thus, in single-target mode, the total time required is 5 seconds.

In multi-target mode:

  • After one second, the health points of the enemies are: [1,1,3,0,0]. Enemies 4 and 5 are dead after one second.
  • After two seconds, the health points of the enemies are: [0,0,2,0,0].
  • After three seconds, the health points of the enemies are: [0,0,1,0,0].
  • After four seconds, the health points of the enemies are: [0,0,0,0,0].

Thus, 4 seconds are required to kill enemies using multi-target mode. The minimum time required to kill all the enemies is 4 seconds.

Test case 2: In single-target mode, all enemies can be killed in 1 second each. Thus, in single-target mode, the total time required is 3 seconds.

In multi-target mode:

Infernos solution codechef

  • After one second, the health points of the enemies are: [4,3,4].
  • After two seconds, the health points of the enemies are: [3,2,3].
  • After three seconds, the health points of the enemies are: [2,1,2].
  • After four seconds, the health points of the enemies are: [1,0,1].
  • After five seconds, the health points of the enemies are: [0,0,0].

Thus, 5 seconds are required to kill enemies using multi-target mode. The minimum time required to kill all the enemies is 3 seconds.

Test case 3: Here, single-target mode will take 4 seconds and multi-target mode will also take 4 seconds. Therefore, the minimum time required is 4 seconds.

Test case 4: Here, single-target mode will take 3 seconds, while multi-target mode will take 9 seconds. Therefore, the minimum time required is 3 seconds.

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