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();
            long ret = long.MaxValue;
            for (int i = 0; i < x[0]; i++)//魔法使用回数制限
            {
                long now = 0;
                for (int j = 0; j < x[0]; j++)//スライム決め
                {
                    int min = a[j];
                    for (int k = 0; k <= i; k++)//魔法使用回数
                    {
                        min = Math.Min(min,a[(j - k + x[0]) % x[0]]);
                    }
                    now += min;
                }
                ret = Math.Min(ret,now + x[1] * i);
            }
            Console.WriteLine(ret);
        }
    }
}