You are fighting N monsters. The i-th monster has H[i] health points.

You have K attacks available per second. In every second, you can distribute these attacks among the monsters. Each attack decreases the health of one monster by 1.

A monster is killed when its health becomes 0.

Determine the minimum number of seconds required to kill all monsters.

Input Format

The first line contains two integers:

N K

The second line contains N integers:

H[1] H[2] ... H[N]

Output Format

Print the minimum number of seconds required to kill all monsters.

Constraints

1 ≤ N ≤ 2 × 10^5 1 ≤ K ≤ 10^9 1 ≤ H[i] ≤ 10^9

Example

Input: 3 4 5 3 6

Output: 4

Explanation:

Total health:

5 + 3 + 6 = 14

You can perform 4 attacks per second, so at least:

ceil(14 / 4) = 4

seconds are required.

It is possible to distribute the attacks so that all monsters are killed within 4 seconds.

Therefore, the answer is:

4