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>
const long long MXN = 3e5 + 1;
const long long MNN = 1e3 + 1;
const long long MOD = 998244353;
const long long INF = 1e18;
const long long OO = 1e9 + 500;
using namespace std;
long long n, b[MXN], x, mxx, ans;
int main() {
  ios_base::sync_with_stdio(0), cout.tie(0), cin.tie(0);
  ;
  cin >> n >> x;
  for (int i = 1; i <= n; i++) {
    cin >> b[i];
  }
  for (int i = 1; i <= n; i++) {
    long long mn = INF, k = 0, mx = 0;
    for (int j = 1; j <= n; j++) {
      if (i >= j) {
        if (mn > (i - j) * x + b[j]) {
          mn = (i - j) * x + b[j];
          mx = i - j;
          k = b[j];
        }
      } else {
        if (mn > (n - (j - i)) * x + b[j]) {
          mn = (n - (j - i)) * x + b[j];
          k = b[j];
          mx = n - j + i;
        }
      }
    }
    mxx = max(mxx, mx);
    ans += k;
  }
  cout << ans + mxx * x;
  return 0;
}
