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>
 
int main()
{
  std::ios::sync_with_stdio(false);
  std::cin.tie(0);
  
  long n, x;
  std::cin >> n >> x;
  long a[n];
  for(int i = 0; i < n; ++i)
  {
    long _a;
    std::cin >> _a;
    a[i] = _a;
  }
  
  long magic = 0;
  long c[n] = {0};
  long cost[n] = {0};
  for(int i = 0; i < n; ++i)
  {
    for(int j = 0; j < n; ++j)
    {
      long _c = x * i + a[(j + i) % n];
      if(i == 0 || cost[j] > _c)
      {
        magic = i;
        cost[j] = _c;
        c[j] = a[(j + i) % n];
      }
    }
  }

  long s = magic * x;
  for(int i = 0; i < n; ++i)
  {
    s += c[i];
  }
  
  std::cout << s;
      
  return 0;
}