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;

class AGC004
{
    static void Main(string[] args) {
        var spl = Console.ReadLine().Split();
        long N = long.Parse(spl[0]);
        long x = long.Parse(spl[1]);
        var a = Console.ReadLine().Split().Select(long.Parse).ToArray();

        long res = 0;
        long xTimeMax = 0;
        for (long i = 0; i < N; i++) {
            long min = long.MaxValue;
            long xTimeTemp = long.MaxValue;
            for (long xTime = 0; xTime < N; xTime++) {
                long back = (i - xTime + N) % N;
                if(min > x* xTime + a[back]) {
                    xTimeTemp = xTime;
                    min = a[back];
                }
                //min = Math.Min(min, x * xTime + a[back]);
            }
            res += min;
            xTimeMax = Math.Max(xTimeMax, xTimeTemp);
        }
        res += x * xTimeMax;
        
        Console.WriteLine(res);
    }
}