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 MX = 4010;
const long long inf = 2e17;
int n, A[MX];
long long B[MX], mn[MX], ans, x;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> x;
  for (int i = 1; i <= n; i++) cin >> A[i];
  for (int i = 1; i <= 2 * n; i++) B[i] = A[(i - 1) % n + 1] + x * (2 * n - i);
  mn[1] = 1;
  for (int i = 2; i <= 2 * n; i++)
    if (B[mn[i - 1]] >= B[i])
      mn[i] = i;
    else
      mn[i] = mn[i - 1];
  int mx = 0;
  for (int i = 1; i <= n; i++) {
    int j = mn[i + n];
    mx = max(mx, i + n - j);
    ans += A[(j - 1) % n + 1];
  }
  ans += mx * x;
  cout << ans;
  return 0;
}
