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() {
  int n, m;
  cin >> n >> m;
  pair<int, int> mn = pair<int, int>(1e9 + 10, 0);
  vector<int> v(n);
  vector<int> ans(n);
  for (int i = 0; i < (int)(n); i++) {
    cin >> v[i];
    ans[i] = v[i];
    mn = min(mn, pair<int, int>(v[i], i));
  }
  int id = mn.second;
  int mx = 0;
  for (int j = 0; j < (int)(n); j++) {
    if (v[(id + 1) % n] > v[id] + m) {
      v[(id + 1) % n] = v[id] + m;
      ans[(id + 1) % n] = ans[id];
      mx = (id + 1 + n - mn.second) % n;
    }
    id = (id + 1) % n;
  }
  long long int s = m * mx;
  for (int i = 0; i < (int)(n); i++) {
    s += ans[i];
  }
  cout << s << endl;
}
