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.Linq;

namespace agc004_b
{
    class Program
    {
        static void Main(string[] args)
        {
            int[] x = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int[] a = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int n = x[0];
            long[,] time = new long[n,n];
            for (int i = 0; i < n; i++)//スライム決め
            {
                int min = a[i];
                for (int j = 0; j < n; j++)//魔法使用回数
                {
                    min = Math.Min(min,a[(i - j + n) % n]);
                    time[i,j] = min;
                }
            }
            long ret = long.MaxValue;
            for (int i = 0; i < n; i++)
            {
                long now = 0;
                for (int j = 0; j < n; j++)
                {
                    now += time[j,i];
                }
                ret = Math.Min(ret,now + x[1] * i);
            }
            Console.WriteLine(ret);
        }
    }
}