Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

B. Settlers' Training

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIn a strategic computer game "Settlers II" one has to build defense structures to expand and protect the territory. Let's take one of these buildings. At the moment the defense structure accommodates exactly *n* soldiers. Within this task we can assume that the number of soldiers in the defense structure won't either increase or decrease.

Every soldier has a rank — some natural number from 1 to *k*. 1 stands for a private and *k* stands for a general. The higher the rank of the soldier is, the better he fights. Therefore, the player profits from having the soldiers of the highest possible rank.

To increase the ranks of soldiers they need to train. But the soldiers won't train for free, and each training session requires one golden coin. On each training session all the *n* soldiers are present.

At the end of each training session the soldiers' ranks increase as follows. First all the soldiers are divided into groups with the same rank, so that the least possible number of groups is formed. Then, within each of the groups where the soldiers below the rank *k* are present, exactly one soldier increases his rank by one.

You know the ranks of all *n* soldiers at the moment. Determine the number of golden coins that are needed to increase the ranks of all the soldiers to the rank *k*.

Input

The first line contains two integers *n* and *k* (1 ≤ *n*, *k* ≤ 100). They represent the number of soldiers and the number of different ranks correspondingly. The second line contains *n* numbers in the non-decreasing order. The *i*-th of them, *a*_{i}, represents the rank of the *i*-th soldier in the defense building (1 ≤ *i* ≤ *n*, 1 ≤ *a*_{i} ≤ *k*).

Output

Print a single integer — the number of golden coins needed to raise all the soldiers to the maximal rank.

Examples

Input

4 4

1 2 2 3

Output

4

Input

4 3

1 1 1 1

Output

5

Note

In the first example the ranks will be raised in the following manner:

1 2 2 3 → 2 2 3 4 → 2 3 4 4 → 3 4 4 4 → 4 4 4 4

Thus totals to 4 training sessions that require 4 golden coins.

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/28/2017 05:27:31 (c3).

Desktop version, switch to mobile version.
User lists

Name |
---|