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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
class Solve{
    public int n;
    public long x;
    public long[] a;
    public Solve(){}
    public static int Main(){
        new Solve().Calc();
        return 0;
    }
    void Calc(){
        getinput();
        long[] bonus = new long[n-1];
        long ans = 0;
        long temp;
        for(int i = 0;i < n-1;i++){
            bonus[i] = 0;
        }
        for(int i = 0;i < n;i++){
            long min;
            min = a[i];
            for(int j = 1;j < i+1;j++){
                if(min > a[i-j]){
                    bonus[j-1] += min - a[i-j];
                    min = a[i-j];
                }
            }
            for(int j = i+1;j < n;j++){
                if(min > a[i-j+n]){
                    bonus[j-1] += min - a[i-j+n];
                    min = a[i-j+n];
                }
            }
        }
        for(int i = 0;i < n;i++){
            ans += a[i];
        }
        temp = ans;
        for(int i = 0;i < n-1;i++){
            temp += x;
            temp -= bonus[i];
            if(ans > temp){
                ans = temp;
            }
        }
        Console.WriteLine(ans);
    }
    void getinput(){
        string[] str = Console.ReadLine().Split(' ');
        n = int.Parse(str[0]);
        x = int.Parse(str[1]);
        str = Console.ReadLine().Split(' ');
        a = new long[n];
        for (int i = 0; i < n; i++)
        {
            a[i] = int.Parse(str[i]);
        }
    }    
}