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;

namespace b
{
    class Program
    {
        static long n;
        static void Main(string[] args)
        {
            long[] nx = Console.ReadLine().Split().Select(long.Parse).ToArray();
            long[] a = Console.ReadLine().Split().Select(long.Parse).ToArray();
            n = nx[0];
            long x = nx[1];
            long[,] data = new long[n, n];
            long ans = 0;

            for (int i = 0; i < n; i++)
            {
                data[0, i] = a[i];
                ans += a[i];
            }
            for (int magic = 1; magic < n; magic++)
            {
                long tmp = 0;
                for (int slime = 0; slime < n; slime++)
                {
                    data[magic, slime] =
                        Math.Min(data[magic - 1, slime], 
                        data[magic - 1, fixNum(slime - magic)]);
                    tmp += data[magic, slime];
                }
                tmp += magic * x;
                ans = Math.Min(ans, tmp);
            }
            Console.WriteLine(ans);
        }

        static long fixNum(long i)
        {
            if (i < 0) return i + n;
            return i;
        }
    }
}
