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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace tes
{
	class contest
	{
		static void Main(string[] args)
		{
			 var input = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            var list = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
            var memo = new long[list.Length];
            var turnMemo = new int[list.Length];
            
            
            for(int i =input[0]-1; i>=0; i--)
            {
                for(int j =1; j<input[0];j++)
                {
                    int ind = (i + j >= input[0]) ? i + j - input[0] : i + j;

                    if (ind < i)
                    {
                        if (list[i] > list[ind] + (i - ind) * input[1]) turnMemo[i] = i - ind;
                        list[i] = Math.Min(list[i], list[ind] + (i - ind) * input[1]);
                    }
                    else
                    {
                        if (list[i] > list[ind] + (input[0] - ind) * input[1]) turnMemo[i] = input[0] - ind;
                        list[i] = Math.Min(list[i], list[ind] + (input[0] - ind) * input[1]);
                    }
                }
            }

           long max = turnMemo.Max();
            int index = Array.IndexOf(turnMemo, turnMemo.Max());
            long amount = 0;
            for(int i =0; i<input[0]; i++)
            {
                if (i == index) amount += list[i];
                else if(turnMemo[i]==0)amount += list[i] ;
                else amount += list[i] % input[1];
            }




            Console.WriteLine(amount);

		}

	}
}