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.