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.

Examples

Input

2 10
1 100


Output

12


Input

3 10
100 1 100


Output

23


Input

4 10
1 2 3 4


Output

10
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();
            long amount = 0;
            for(int i =0; i<input[0]; i++)
            {
                if (turnMemo[i] == max) amount += list[i];
                else if(turnMemo[i]==0)amount += list[i] ;
                else amount += list[i] % input[1];
            }


            Console.WriteLine(amount);

		}

	}
}