Competitive programming is awesome, but bartending can be a better way to make some extra cash. Tonight you're bartending at the "Lonely Goose" bar at Waterloo, serving their signature "Lonely Goose" cocktail. There are $n$ glasses lined up in a row at a bar table. Initially, all glasses are empty and the goal is to have $a_i$ millilitres of "Lonely Goose" in the $i$-th glass. You're a skilled bartender, and each minute you can choose a contiguous set of glasses and pour either one millilitre of cocktail into each glass or $x$ millilitres into each glass. It is forbidden to pour out excess liquid from a glass (which would be wasteful).

Find out the quickest time in which you can achieve the desired drink allocation.

Input Specification

The first row contains two integers - $n$ and $x$. The next row contains $n$ integers $a_i$.

$1\le n\le 300000,2\le x\le {10}^9,0\le a_i\le {10}^9$

Output Specification

Output a single number - the smallest possible number of minutes to achieve the goal.

Sample Input 1

6 3
1 1 1 4 3 3

Sample Output 1

2

Explanation for Sample 1

In the first test, you can pour 1 millilitre into glasses 1-4, followed by pouring 3 millilitres into glasses 4-6.

Sample Input 2

5 5
4 0 4 0 4

Sample Output 2

12