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;
using lli = long long int;
template <class T, class U>
void init_n(vector<T>& v, size_t n, U x) {
  v = vector<T>(n, x);
}
template <class T>
void init_n(vector<T>& v, size_t n) {
  init_n(v, n, T());
}
template <class T>
void read_n(vector<T>& v, size_t n, size_t o = 0) {
  v = vector<T>(n + o);
  for (lli i = o; i < n + o; ++i) cin >> v[i];
}
template <class T>
void read_n(T a[], size_t n, size_t o = 0) {
  for (lli i = o; i < n + o; ++i) cin >> a[i];
}
template <class T>
T gabs(const T& x) {
  return max(x, -x);
}
lli n, x, a[2000];
int main() {
  cin >> n >> x;
  read_n(a, n);
  lli ans = 1e18;
  for (lli d = 0; d < n; ++d) {
    lli scr = d * x;
    for (lli i = 0; i < n; ++i) {
      a[i] = min(a[i], a[(n + i - d) % n]);
      scr += a[i];
    }
    ans = min(ans, scr);
  }
  cout << ans << '\n';
  return 0;
}
