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>
using namespace std;
int main() {
  long long n, x, ans = 0;
  cin >> n >> x;
  vector<long long> v(n);
  for (int(i) = (0); (i) < (n); ++i) cin >> v[i];
  long long maho = 0;
  for (int(i) = (0); (i) < (n); ++i) {
    if (v[i] <= x)
      ans += v[i];
    else {
      long long tmp = 1000000000000000;
      long long p = (i + n - 1) % n;
      long long k = 1, memo = p, memo1 = 0;
      while (p != i) {
        if (tmp > v[p] + x * k) {
          tmp = v[p] + x * k;
          memo = p;
          memo1 = k;
        }
        p = (p + n - 1) % n;
        k++;
      }
      if (tmp < v[i]) {
        ans += v[memo];
        maho = max(maho, memo1);
      } else
        ans += v[i];
    }
  }
  ans += x * maho;
  cout << ans << endl;
  return 0;
}
