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;
const double pi = 4 * atan(1.0);
constexpr long long mod = static_cast<long long>(1e9 + 7);
using cEdges = vector<vector<int>>;
int main() {
  int N, x;
  cin >> N >> x;
  vector<int> arr(N);
  for (auto& val : arr) cin >> val;
  long long ans = 0;
  auto min_elem = min_element(begin(arr), end(arr));
  int min_index = min_elem - begin(arr);
  ans += arr[min_index];
  int index = (min_index == N - 1 ? 0 : min_index + 1);
  int cnt = 0;
  while (index != min_index) {
    ans += min(arr[index], arr[min_index] + x);
    index = (index == N - 1 ? 0 : index + 1);
  }
  cout << ans << endl;
  return 0;
}
