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;
template <typename _KTy, typename _Ty>
ostream& operator<<(ostream& ostr, const pair<_KTy, _Ty>& m) {
  ostr << "{" << m.first << ", " << m.second << "}";
  return ostr;
}
template <typename _KTy, typename _Ty>
ostream& operator<<(ostream& ostr, const map<_KTy, _Ty>& m) {
  if (m.empty()) {
    ostr << "{ }";
    return ostr;
  }
  ostr << "{" << *m.begin();
  for (auto itr = ++m.begin(); itr != m.end(); itr++) {
    ostr << ", " << *itr;
  }
  ostr << "}";
  return ostr;
}
template <typename _KTy, typename _Ty>
ostream& operator<<(ostream& ostr, const unordered_map<_KTy, _Ty>& m) {
  if (m.empty()) {
    ostr << "{ }";
    return ostr;
  }
  ostr << "{" << *m.begin();
  for (auto itr = ++m.begin(); itr != m.end(); itr++) {
    ostr << ", " << *itr;
  }
  ostr << "}";
  return ostr;
}
template <typename _Ty>
ostream& operator<<(ostream& ostr, const vector<_Ty>& v) {
  if (v.empty()) {
    ostr << "{ }";
    return ostr;
  }
  ostr << "{" << v.front();
  for (auto itr = ++v.begin(); itr != v.end(); itr++) {
    ostr << ", " << *itr;
  }
  ostr << "}";
  return ostr;
}
template <typename _Ty>
ostream& operator<<(ostream& ostr, const set<_Ty>& s) {
  if (s.empty()) {
    ostr << "{ }";
    return ostr;
  }
  ostr << "{" << *(s.begin());
  for (auto itr = ++s.begin(); itr != s.end(); itr++) {
    ostr << ", " << *itr;
  }
  ostr << "}";
  return ostr;
}
template <typename _Ty>
ostream& operator<<(ostream& ostr, const unordered_set<_Ty>& s) {
  if (s.empty()) {
    ostr << "{ }";
    return ostr;
  }
  ostr << "{" << *(s.begin());
  for (auto itr = ++s.begin(); itr != s.end(); itr++) {
    ostr << ", " << *itr;
  }
  ostr << "}";
  return ostr;
}
template <typename _Ty>
ostream& operator<<(ostream& ostr, const stack<_Ty>& s) {
  if (s.empty()) {
    ostr << "{ }";
    return ostr;
  }
  stack<_Ty> t(s);
  ostr << "{" << t.top();
  t.pop();
  while (!t.empty()) {
    ostr << ", " << t.top();
    t.pop();
  }
  ostr << "}";
  return ostr;
}
template <typename _Ty>
ostream& operator<<(ostream& ostr, const list<_Ty>& l) {
  if (l.empty()) {
    ostr << "{ }";
    return ostr;
  }
  ostr << "{" << l.front();
  for (auto itr = ++l.begin(); itr != l.end(); ++itr) {
    ostr << ", " << *itr;
  }
  ostr << "}";
  return ostr;
}
template <typename _KTy, typename _Ty>
istream& operator>>(istream& istr, pair<_KTy, _Ty>& m) {
  istr >> m.first >> m.second;
  return istr;
}
template <typename _Ty>
istream& operator>>(istream& istr, vector<_Ty>& v) {
  for (size_t i = 0; i < v.size(); i++) istr >> v[i];
  return istr;
}
namespace aux {
template <typename Ty, unsigned N, unsigned L>
struct tp {
  static void print(ostream& os, const Ty& v) {
    os << get<N>(v) << ", ";
    tp<Ty, N + 1, L>::print(os, v);
  }
};
template <typename Ty, unsigned N>
struct tp<Ty, N, N> {
  static void print(ostream& os, const Ty& value) { os << get<N>(value); }
};
}  // namespace aux
template <typename... Tys>
ostream& operator<<(ostream& os, const tuple<Tys...>& t) {
  os << "{";
  aux::tp<tuple<Tys...>, 0, sizeof...(Tys) - 1>::print(os, t);
  os << "}";
  return os;
}
template <typename A, size_t N, typename T>
inline void Fill(A (&array)[N], const T& val) {
  std::fill((T*)array, (T*)(array + N), val);
}
void dump_func() { cerr << endl; }
template <class Head, class... Tail>
void dump_func(Head&& head, Tail&&... tail) {
  cerr << head;
  if (sizeof...(Tail) == 0) {
    cerr << " ";
  } else {
    cerr << ", ";
  }
  dump_func(std::move(tail)...);
}
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  long long N, x;
  cin >> N >> x;
  vector<long long> a(N);
  cin >> a;
  long long ans = INT64_MAX;
  for (long long idx = 0; idx < N; idx++) {
    long long selected_a = a[idx];
    long long cost = selected_a;
    for (long long i = idx + 1; i < idx + N; i++) {
      long long n = i % N;
      if (x + selected_a < a[n])
        cost += x + a[idx];
      else
        cost += a[n];
    }
    ans = min(ans, cost);
  }
  cout << ans << endl;
  return 0;
}
