Sequence Transformation

The math teacher dislikes Kolya very much and always makes him answer at the blackboard with the hardest problems.

Today she wrote a sequence of $n$ non-negative integers $a_1, a_2, \ldots, a_n$ on the blackboard and called Kolya up. In one action, the teacher allows Kolya to erase any number and write in its place a number one greater. The teacher demands that Kolya, in the minimum number of actions, make the numbers 1 through $h$ appear consecutively somewhere in this sequence.

Help Kolya find the minimum number of actions needed so that for some $i$, $a_i=1$, $a_{i+1}=2$, ..., $a_{i+h-1}=h$, or determine that this is impossible and the teacher is again bullying poor Kolya with impunity.

The first line of the input file contains two positive integers: $n$ and $h$ ($1 \le h \le n \le 200\,000$). The second line contains $n$ numbers $a_i$, the initial values of the sequence ($0 \le a_{i} \le n$).

In a single line of the output file, print the minimum number of actions with which Kolya can complete the task, or $-1$ if it is impossible.

In the first example, Kolya must increase the third number by 1 twice and the fourth number once. Then the sequence becomes 1, 1, 2, 3, and for $i=2$ the required condition holds.

In the second example, it is impossible to obtain 1 and 2 consecutively in the sequence.