Problem:
Score : 400 points

Problem Statement

Snuke lives in another world, where slimes are real creatures and kept by some people.
Slimes come in N colors. Those colors are conveniently numbered 1 through N.
Snuke currently has no slime. His objective is to have slimes of all the colors together.

Snuke can perform the following two actions:

Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.

Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.

Find the minimum time that Snuke needs to have slimes in all N colors.

Constraints

2≤N≤2,000

a_i are integers.

1≤a_i≤10^9

x is an integer.

1≤x≤10^9

Input

The input is given from Standard Input in the following format:

N x
a_1 a_2 ... a_N

Output

Find the minimum time that Snuke needs to have slimes in all N colors.

Sample Input 1

2 10
1 100

Sample Output 1

12

Snuke can act as follows:

Catch a slime in color 1. This takes 1 second.

Cast the spell. The color of the slime changes: 1 → 2. This takes 10 seconds.

Catch a slime in color 1. This takes 1 second.

Sample Input 2

3 10
100 1 100

Sample Output 2

23

Snuke can act as follows:

Catch a slime in color 2. This takes 1 second.

Cast the spell. The color of the slime changes: 2 → 3. This takes 10 seconds.

Catch a slime in color 2. This takes 1 second.

Cast the soell. The color of each slime changes: 3 → 1, 2 → 3. This takes 10 seconds.

Catch a slime in color 2. This takes 1 second.

Sample Input 3

4 10
1 2 3 4

Sample Output 3

10

Snuke can act as follows:

Catch a slime in color 1. This takes 1 second.

Catch a slime in color 2. This takes 2 seconds.

Catch a slime in color 3. This takes 3 seconds.

Catch a slime in color 4. This takes 4 seconds.

Solution in Kotlin (1.0.0) (judge verdict: Wrong Answer)

import java.util.Scanner

fun main(args: Array<String>){
  val scn = Scanner(System.`in`) //Scannerのインスタンスを作成
  val n: Int = scn.nextInt()//Int型に変換
  val x: Int = scn.nextInt()
  
  val a: MutableList<Int>  = mutableListOf()
  
  var count = n
  while(0 < count--) {
    val t = scn.nextInt()
    a.add(t)
  }

  var memo = Array(n, {i -> Array(n, { j-> 0 }) })
  
  var id = n
  while(0 < id--) {
    var i = n - id - 1
    var rec = -1
    var jd = n
    while(0 < jd--) {
      var j = n - jd - 1
      var k = (n + i - j) % n
      if (rec < 0 || a[k] < rec) {
        rec = a[k]
      }
      memo[i][j] = rec
    }
  }
    
  var record = -1
  
  var jd = n
  while(0 < jd--) {
    var j = n - jd - 1
    var temp = x * j
    
    var id = n
    while(0 < id--) {
      var i = n - id - 1
      temp = temp + memo[i][j]
    }
    if ( record < 0 || temp < record) {
      record = temp
    }
  }
  
  println(record)
}