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;
template <class S, class T>
istream& operator>>(istream& is, pair<S, T>& p) {
  return is >> p.first >> p.second;
}
const double EPS = 1e-10;
const double PI = acos(-1.0);
const long long MOD = 1e9 + 7;
int main() {
  cin.tie(0);
  ios_base::sync_with_stdio(false);
  long long N, X;
  cin >> N >> X;
  vector<long long> xs(N);
  for (int i = (0); i < (N); ++i) cin >> xs[i];
  long long ans = 1e18;
  for (int d = (0); d < (N); ++d) {
    long long s = 0;
    for (int i = (0); i < (N); ++i) {
      xs[i] = min(xs[i], xs[(i - d + N) % N]);
      s += xs[i];
    }
    ans = min(ans, s + X * d);
  }
  cout << ans << endl;
  return 0;
}
