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;
void init_ios() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
}
const long long N = 2010;
long long n, a[N], x, res = 1e18;
long long pref[N], suf[N];
signed main() {
  init_ios();
  cin >> n >> x;
  for (long long i = 1; i <= n; ++i) {
    cin >> a[i];
    pref[i] = pref[i - 1] + a[i];
  }
  for (long long i = n; i >= 1; --i) suf[i] = suf[i + 1] + a[i];
  for (long long dl = 1; dl <= n; ++dl) {
    long long tmp = 1e18;
    for (long long s = 1; s <= n; ++s) {
      long long ile = suf[s] - suf[s + dl];
      if (s + dl - 1 > n) ile += pref[s + dl - n - 1];
      ile += (n - dl) * (x + a[s]);
      res = min(res, ile);
    }
  }
  cout << res << "\n";
}
