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(void) {
  long long a[2010], i, j, n, x, tmp, ans = 0, dif, p, q, t, wait = 0, cnt = 1;
  cin >> n >> x;
  for (i = 0; i < n; i++) {
    cin >> a[i];
  }
  for (i = 0; i < n; i++) {
    tmp = (1ll << 60);
    for (j = 0; j < n; j++) {
      dif = (i - j + n) % n;
      t = a[j] + dif * x;
      if (t < tmp) {
        p = j;
        q = dif;
        tmp = t;
      }
    }
    ans += a[p];
    if (wait == q) {
      cnt++;
    } else if (wait < q) {
      wait = q;
      cnt = 1;
    }
    wait = max(wait, q);
  }
  ans += ((wait * x) * cnt);
  cout << ans << endl;
  return 0;
}
