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();

      bool[] b = new bool[N];

      ulong ans = 0;
      while (true)
      {
        bool isAll = true;
        bool isAllFalse = true;
        for (ulong i = 0; i < N; i++)
        {
          if (b[i])
          {
            isAllFalse = false;
          }
          if(!b[i])
          {
            isAll = false;
          }
        }
        if (isAll)
        {
          break;
        }

        ulong minIndex = INF;
        for (ulong i = 0; i < N; i++)
        {
          if (b[i])
          {
            continue;
          }
          if (minIndex == INF || a[i] < a[minIndex])
          {
            minIndex = i;
          }
        }
        if (isAllFalse) 
        {
          ans += a[minIndex];
          b[minIndex] = true;
          continue;
        }

        if (a[minIndex] < x) 
        {
          ans += a[minIndex];
          b[minIndex] = true;
        }
        else
        {
          ans += x;
          bool bN = b[N - 1];
          for (ulong i = N - 1; i > 0; i--)
          {
            b[i] = b[i - 1];
          }
          b[0] = bN;
        }

      }

      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();
    }
  }
}