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;
using System.Linq;
using System.Text;

namespace b
{
    class Program
    {
        static long n;
        static void Main(string[] args)
        {
            long[] nx = Console.ReadLine().Split().Select(long.Parse).ToArray();
            long[] a = Console.ReadLine().Split().Select(long.Parse).ToArray();
            n = nx[0];
            long x = nx[1];
            long[,] data = new long[n, n];
            long ans = 0;

            for (long i = 0; i < n; i++)
            {
                data[0, i] = a[i];
                ans += a[i];
            }
            for (long magic = 1; magic < n; magic++)
            {
                long tmp = magic * x;
                for (long slime = 0; slime < n; slime++)
                {
                    data[magic, slime] =
                        Math.Min(data[magic - 1, slime], 
                        data[0, fixNum(slime - magic)]);
                    tmp += data[magic, slime];
                }
                ans = Math.Min(ans, tmp);
            }
            Console.WriteLine(ans);
        }

        static long fixNum(long i)
        {
            if (i < 0) return i + n;
            return i;
        }
    }
}