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;
long long a[2005];
long long aa[2005];
signed main() {
  long long n, x;
  cin >> n >> x;
  for (long long(i) = (0); (i) <= (n - 1); (i)++) cin >> a[i];
  long long rot = 0;
  for (long long(i) = (0); (i) <= (n - 1); (i)++) {
    long long r = -1;
    long long cost = 123456789012345;
    for (long long(j) = (0); (j) <= (n - 1); (j)++) {
      long long c = a[j] + ((i - j + n) % n) * x;
      if (c <= cost) {
        if (c == cost && r > (i - j + n) % n) continue;
        r = (i - j + n) % n;
        cost = c;
        aa[i] = a[j];
      }
    }
    rot = max(rot, r);
  }
  long long ans = 0;
  for (long long(i) = (0); (i) <= (n - 1); (i)++) ans += aa[i];
  ans += rot * x;
  cout << ans << endl;
}
