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 uint = unsigned;
using ll = long long;
using ull = unsigned long long;
using vi = vector<int>;
using vvi = vector<vi>;
using vl = vector<ll>;
using vvl = vector<vl>;
using vd = vector<double>;
using vvd = vector<vd>;
using vs = vector<string>;
using pii = pair<int, int>;
template <typename T1, typename T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
  return os << '(' << p.first << ',' << p.second << ')';
}
template <typename Tuple>
void print_tuple(ostream&, const Tuple&) {}
template <typename Car, typename... Cdr, typename Tuple>
void print_tuple(ostream& os, const Tuple& t) {
  print_tuple<Cdr...>(os, t);
  os << (sizeof...(Cdr) ? "," : "") << get<sizeof...(Cdr)>(t);
}
template <typename... Args>
ostream& operator<<(ostream& os, const tuple<Args...>& t) {
  print_tuple<Args...>(os << '(', t);
  return os << ')';
}
template <typename Ch, typename Tr, typename C>
basic_ostream<Ch, Tr>& operator<<(basic_ostream<Ch, Tr>& os, const C& c) {
  os << '[';
  for (auto i = begin(c); i != end(c); ++i)
    os << (i == begin(c) ? "" : " ") << *i;
  return os << ']';
}
constexpr int INF = 1e9;
constexpr int MOD = 1e9 + 7;
constexpr double EPS = 1e-9;
int main() {
  for (int n, x; cin >> n >> x && n | x;) {
    vi a(n);
    for (int i = int(0); i < int(n); i++) cin >> a[i];
    ll res = 0;
    for (int i = int(0); i < int(n); i++) {
      int mn = INF;
      for (int j = int(0); j < int(n); j++)
        mn = min(mn, a[j] + (i - j + n) % n * x);
      res += mn;
    }
    cout << res << endl;
  }
}
