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;
using ll = long long;
int main() {
  ll n, x;
  cin >> n >> x;
  ll a[n];
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  ll ans = 0;
  priority_queue<int> allmagic;
  for (int i = 0; i < n; i++) {
    ll finish = 9223372036854775807;
    ll capt = 0;
    ll magic = 0;
    for (int j = 0; j < n; j++) {
      ll temp;
      if (i > j) {
        temp = (i - j) * x + a[j];
      } else if (i == j) {
        temp = a[j];
      } else {
        temp = (n - (j - i)) * x + a[j];
      }
      if (finish > temp) {
        finish = temp;
        capt = a[j];
        if (i >= j) {
          magic = i - j;
        } else {
          magic = n - j + i;
        }
      }
    }
    ans += capt;
    allmagic.push(magic);
  }
  cout << ans + x * allmagic.top() << endl;
}
