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 long long inf = 1e9 + 7;
const long long N = 2001;
long long n, a[N], ans = 0, t[N] = {0}, x;
long long mina = inf, minai;
int main() {
  cin >> n >> x;
  for (long long i = (0); i < (n); ++i) {
    cin >> a[i];
    t[i] = a[i];
    if (a[i] < mina) {
      minai = i;
    }
  }
  for (long long i = (0); i < (n); ++i) {
    for (long long j = (1); j < (n); ++j) {
      long long k;
      if (j <= i)
        k = i - j;
      else
        k = n - (j - i);
      t[i] = min(t[i], t[(i + j) % n] + x * k);
    }
  }
  for (long long i = (0); i < (n); ++i) ans += t[i];
  cout << ans << endl;
}
