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 AGC004_B3
{
    class Program
    {
        static int N, x;
        static void Main(string[] args)
        {
            var t = scan;
            N = t[0]; x = t[1];
            var a = scan;
            var b = new int[N];
            for (int i = 0; i < N; i++)
            {
                b[i] = a[i];
            }

            long ans = a.Sum();
            for (int k = 1; k < N; k++)
            {
                long time = (long)k * x;

                for (int i = 0; i < N; i++)
                {
                    int p = (i - k < 0) ? i - k + N : i - k;
                    b[i] = Math.Min(b[i], a[p]);
                    time += b[i];
                }
                ans = Math.Min(ans, time);
            }
            Console.WriteLine(ans);
        }

        static int[] scan { get { return Array.ConvertAll(Console.ReadLine().Split(), int.Parse); } }
    }
}
