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 <typename T>
istream& operator>>(istream& is, vector<T>& v) {
  for (auto& x : v) {
    is >> x;
  }
  return is;
}
template <typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
  for (auto& x : v) {
    os << x << " ";
  }
  os << "\n";
  return os;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n;
  uint64_t x;
  cin >> n >> x;
  vector<uint64_t> a(n);
  cin >> a;
  uint64_t min_ans = 0;
  for (auto i : a) min_ans += i;
  for (auto max_j = 1; max_j < n; ++max_j) {
    vector<uint64_t> b = a;
    for (int i = 0; i < n; ++i) {
      for (int j = 1; j <= max_j; ++j) {
        uint64_t cur = a[(n + i - j) % n];
        if (cur < b[i]) b[i] = cur;
      }
    }
    uint64_t cur_ans = max_j * x;
    for (auto i : b) cur_ans += i;
    if (cur_ans < min_ans) min_ans = cur_ans;
  }
  cout << min_ans << "\n";
}
