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;
template <class T>
using pque_max = priority_queue<T>;
template <class T>
using pque_min = priority_queue<T, vector<T>, greater<T> >;
template <class T>
ostream& operator<<(ostream& os, vector<T> const& v) {
  os << "{";
  for (auto const& x : v) os << " " << x;
  return os << " }";
}
template <class T>
ostream& operator<<(ostream& os, deque<T> const& v) {
  os << "{";
  for (auto const& x : v) os << " " << x;
  return os << " }";
}
template <class T>
ostream& operator<<(ostream& os, set<T> const& v) {
  os << "{";
  for (auto const& x : v) os << " " << x;
  return os << " }";
}
template <class T, class U>
ostream& operator<<(ostream& os, map<T, U> const& v) {
  os << "{";
  for (auto const& x : v) os << " " << x;
  return os << " }";
}
template <class T>
istream& operator>>(istream& is, vector<T>& v) {
  for (auto& x : v) is >> x;
  return is;
}
template <class T, class S>
ostream& operator<<(ostream& os, pair<T, S> const& p) {
  return os << "(" << p.first << ", " << p.second << ")";
}
template <class T, class S>
istream& operator>>(istream& is, pair<T, S> const& p) {
  return is >> p.first >> p.second;
}
struct _Init_ {
  _Init_() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  }
} _init_;
template <class T>
void quit(T const& x) {
  cout << x << endl;
  exit(0);
}
template <class T>
bool chmin(T& x, T const& y) {
  if (x > y) {
    x = y;
    return true;
  }
  return false;
}
template <class T>
bool chmax(T& x, T const& y) {
  if (x < y) {
    x = y;
    return true;
  }
  return false;
}
ll mod(ll x, ll m) { return (x % m + m) % m; }
int32_t main() {
  ll n, x;
  cin >> n >> x;
  vector<ll> a(n);
  cin >> a;
  vector<ll> b = a;
  ll mi = 1e13;
  for (ll k = 0; k < ll(n); k++) {
    for (ll i = 0; i < ll(n); i++) chmin(b[i], a[mod(i - k, n)]);
    chmin(mi, x * k + accumulate((b).begin(), (b).end(), 0));
  }
  cout << mi << endl;
}
