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_B
{
    class Program
    {
        static long[] a;
        static long N, x;
        static long mindex;
        static long ans;
        static void Main(string[] args)
        {
            var t = scan;
            N = t[0];
            x = t[1];
            a = scan;
            mindex = Array.IndexOf(a, a.Min());
            ans += a[mindex]; 

            for (int i = 1; i < N; i++)
            {
                if(mindex + i >= N)
                {
                    ans += Math.Min(a[mindex + i - N], a[mindex] + x);
                }
                else
                {
                    ans += Math.Min(a[mindex + i], a[mindex] + x);
                }
            }
            Console.WriteLine(ans);

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