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 ll = long long;
using ull = decltype(1ull);
template <class T>
int size(T&& a) {
  return a.size();
}
template <class B>
pair<int, B> make_pair(B b) {
  return {0, b};
}
void Calc();
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cin.exceptions(istream::failbit | istream::badbit);
  cout << fixed << setprecision(15);
  Calc();
  cout.flush();
  return 0;
}
template <class A>
void amax(A& a, A b) {
  a = max(a, b);
}
template <class A>
void amin(A& a, A b) {
  a = min(a, b);
}
template <class A>
int comp(A a, A b) {
  return a < b ? 1 : b < a ? -1 : 0;
}
struct Scanner {
  template <class A = string>
  A Next() {
    A a;
    Next(a);
    return a;
  }
  template <class A, class B>
  void Next(pair<A, B>& a) {
    cin >> a.first >> a.second;
  }
  template <class A>
  void Next(A& a) {
    cin >> a;
  }
  template <class A = int>
  vector<A> Array(int n) {
    vector<A> a(n);
    for (A& i : a) (*this), i;
    return a;
  }
  string Line() const {
    string s;
    getline(cin, s);
    return s;
  }
  template <class A>
  Scanner& operator,(A& a) {
    a = Next<A>();
    return *this;
  }
  template <class A>
  operator A() {
    return Next<A>();
  }
} in;
void Calc() {
  int n, x;
  in, n, x;
  ;
  auto a = in.Array(n);
  const ll INFL = 1e18 - 1;
  ll ans = INFL;
  auto minpos = distance(a.begin(), min_element(begin(a), end(a)));
  for (typename make_signed<decltype(make_pair(n + 1).second)>::type
           i = make_pair(n + 1).first,
           _li = make_pair(n + 1).second;
       i < _li; i++) {
    ll tmp = 0;
    for (typename make_signed<decltype(make_pair(n).second)>::type
             j = make_pair(n).first,
             _lj = make_pair(n).second;
         j < _lj; j++) {
      if ((j - minpos + n) % n <= i) {
        tmp += min(a[minpos], a[j]);
      } else {
        tmp += a[j];
      }
    }
    tmp += x * i;
    amin(ans, tmp);
  }
  cout << (ans) << endl;
}
