Infernos CodeChef Solution | CodeChef Problem Solution 2022

Infernos CodeChef Solution | CodeChef Problem Solution 2022

Ved started playing a new mobile game called Fighting Clans. An army of N$N$ enemies is approaching his base. The ith$i^{th}$ enemy has Hi$H_i$ health points. An enemy gets killed if his health points become 0$0$.
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$X$ health points.
• Multi-Target Mode: In one second, the Inferno can target all living enemies and cause damage of 1$1$ health point to each of them.

Find the minimum time required to kill all the enemies.

Solution Click Below:-  CLICK HERE

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

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• The second line of each test case contains N$N$ space-separated integers H1,H2,…,HN$H_1,H_2,\dots ,H_N$ where Hi$H_i$ denotes the initial health points of ith$i^{th}$ enemy.

Output Format

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

Constraints

• 1≤T≤1000$1\le T\le 1000$
• 1≤N≤200$1\le N\le 200$
• 1≤X≤100$1\le X\le 100$
• 1≤Ai≤100$1\le A_i\le 100$

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

Sample Output 1 

4
3
4
3

Explanation

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

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

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

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

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

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

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

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

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