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;
class Solve{
    public int n = 4;
    public long x = 10;
    public long[] a = {1,2,3,4};
    public Solve(){}
    public static int Main(){
        new Solve().Calc();
        return 0;
    }
    void Calc(){
        //getinput();
        long[] bonus = new long[n-1];
        long ans = 0;
        long temp;
        for(int i = 0;i < n-1;i++){
            bonus[i] = 0;
        }
        for(int i = 0;i < n;i++){
            long min;
            min = a[i];
            for(int j = 1;j < i+1;j++){
                if(min > a[i-j]){
                    bonus[j-1] += min - a[i-j];
                }
            }
            for(int j = i+1;j < n;j++){
                if(min > a[i-j+n]){
                    bonus[j-1] += min - a[i-j+n];
                }
            }
        }
        for(int i = 0;i < n;i++){
            ans += a[i];
        }
        temp = ans;
        for(int i = 0;i < n-1;i++){
            temp += x;
            temp -= bonus[i];
            if(ans > temp){
                ans = temp;
            }
        }
        Console.WriteLine(ans);
    }
    void getinput(){
        string[] str = Console.ReadLine().Split(' ');
        n = int.Parse(str[0]);
        x = int.Parse(str[1]);
        str = Console.ReadLine().Split(' ');
        a = new long[n];
        for (int i = 0; i < n; i++)
        {
            a[i] = int.Parse(str[i]);
        }
    }    
}