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;
using System.IO;
using System.Linq;

namespace CompetitiveProgramming
{

  class Solve
  {
    const int INF = (int)(1e9) + 10;

    private void Main()
    {
      ulong[] Nx = Console.ReadLine().Split().Select(ulong.Parse).ToArray();
      ulong N = Nx[0], x = Nx[1];
      ulong[] a = Console.ReadLine().Split().Select(ulong.Parse).ToArray();
      ulong aMin = INF;

      ulong ans = 0;
      for (ulong i = 0; i < N; i++)
      {
        ans += a[i];
        aMin = Math.Min(aMin, a[i]);
      }

      ulong dMax = 0;
      for (ulong i = 0; i < N; i++)
      {
        ulong t = INF;
        ulong dd = 0;
        for (ulong j = 0; j < N; j++)
        {
          ulong d = i - j;
          if (j > i)
          {
            d = N - j;
          }
          ulong tmp = a[j] + d * x;
          if (tmp < t)
          {
            t = tmp;
            dd = d;
          }
        }
        dMax = Math.Max(dMax, dd);
      }
      if (dMax > 0)
      {
        ans = Math.Min(ans, x * dMax + aMin * N);
      }
      Console.WriteLine(ans);
    }

    public Solve()
    {
      Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
      Main();
      Console.Out.Flush();
    }
  }

  class Program
  {
    static void Main(string[] args)
    {
      new Solve();
    }
  }
}