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 <bits/stdc++.h>
int main() {
  long long n, x, p = 0;
  std::cin >> n >> x;
  std::vector<long long> a(n), t(n), magic(n, 0);
  for (long long i = 0; i < n; i++) {
    std::cin >> a[i];
    if (a[p] > a[i]) p = i;
  }
  std::rotate(a.begin(), a.begin() + p, a.end());
  t[0] = a[0];
  long long mnum = 0, ret = 0;
  for (long long i = 1; i < n; i++) {
    if (a[i] >= x + t[i - 1 - magic[i - 1]]) {
      t[i] = t[i - 1] + x;
      magic[i] = magic[i - 1] + 1;
      if (magic[i] > mnum) mnum = magic[i];
    } else {
      t[i] = a[i];
      ret += t[i - 1 - magic[i - 1]] * (magic[i - 1] + 1);
    }
  }
  ret += t[n - 1 - magic[n - 1]] * (magic[n - 1] + 1);
  ret += mnum * x;
  std::cout << ret << std::endl;
  return 0;
}
