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
#include <iostream>
#define ll long long
using namespace std;

int main()
{
  int N, X;
  cin>>N>>X;
  ll a[N];
  ll mn[N];
  for(int i=0; i<N; i++)
  {
    cin>>a[i];
    mn[i] = -1;
  }

  ll answ = -1;
  for(int k=0; k<N; k++)
  {
    ll tot = (ll)X * k; //provo a prendere tutti i possibili k

    for(int i=0; i<N; i++)
    {
      if(mn[i] == -1 || a[(i-k+N)%N] < mn[i])
       mn[i] = a[(i-k+N)%N];
      tot += mn[i];
    }

    if(answ == -1 || tot < answ) answ = tot;
  }

  cout<<answ;
  return 0;
}
