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 ColorfulSlimes
{
    class Program
    {
        static void Main(string[] args)
        {
            int N, x;
            string[] vals = Console.ReadLine().Split(' ');
            N = int.Parse(vals[0]);
            x = int.Parse(vals[1]);
            int[] a = new int[N+1];

            vals = Console.ReadLine().Split(' ');
            for (int i = 1; i <= N; i++)
                a[i] = int.Parse(vals[i-1]);

            int[] b = new int[N + 1];
            long maxSpells = 0;

            for(int i=1; i<= N; i++)
            {
                long mintime = int.MaxValue;
                long spells = 0;
                int k = 0;
                for(int j = 1; j <= N; j++)
                {
                    long m;
                    long t;
                    if(j <= i)
                    {
                        m = i - j;
                    }
                    else
                    {
                        m = (N - j) + i;
                    }
                    t = a[j] + m * x;
                    if(t < mintime)
                    {
                        mintime = t;
                        spells = m;
                        k = j;
                    }
                }
                b[i] = a[k];
                if (spells > maxSpells)
                    maxSpells = spells;
            }

            long ans = 0;
            for (int i = 1; i <= N; i++)
                ans += b[i];
            ans += x * maxSpells;
            Console.WriteLine(ans);
        }
    }
}
