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 int INF = 1145141919, MOD = 1e9 + 7;
const long long LINF = 8101145141919364364, LMOD = 998244353;
int main() {
  int n, x;
  cin >> n >> x;
  int a[n];
  for (int i = 0; i < n; i++) cin >> a[i];
  long long t[n][n];
  for (int from = 0; from < n; from++) {
    for (int to = 0; to < n; to++) {
      if (from <= to) {
        t[from][to] = x * (to - from);
      } else {
        t[from][to] = x * (n - from + to);
      }
    }
  }
  long long summon = 0, trans = 0;
  for (int i = 0; i < n; i++) {
    long long tt = LINF, from;
    for (int j = 0; j < n; j++) {
      if (tt >= a[j] + t[j][i]) {
        tt = a[j] + t[j][i];
        from = j;
      }
    }
    summon += a[from];
    trans = max(trans, t[from][i]);
  }
  cout << summon + trans << endl;
  return 0;
}
