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 T>
void unique(T &c) {
  c.erase(std::unique(c.begin(), c.end()), c.end());
}
template <class T>
bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &vec) {
  for (auto &v : vec) is >> v;
  return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &vec) {
  for (int i = 0; i < vec.size(); i++) {
    os << vec[i];
    if (i + 1 != vec.size()) os << " ";
  }
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const set<T> &st) {
  for (auto itr = st.begin(); itr != st.end(); ++itr) {
    os << *itr;
    auto titr = itr;
    if (++titr != st.end()) os << " ";
  }
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const unordered_set<T> &st) {
  for (auto itr = st.begin(); itr != st.end(); ++itr) {
    os << *itr;
    auto titr = itr;
    if (++titr != st.end()) os << " ";
  }
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const multiset<T> &st) {
  for (auto itr = st.begin(); itr != st.end(); ++itr) {
    os << *itr;
    auto titr = itr;
    if (++titr != st.end()) os << " ";
  }
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const unordered_multiset<T> &st) {
  for (auto itr = st.begin(); itr != st.end(); ++itr) {
    os << *itr;
    auto titr = itr;
    if (++titr != st.end()) os << " ";
  }
  return os;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const map<T1, T2> &mp) {
  for (auto itr = mp.begin(); itr != mp.end(); ++itr) {
    os << "(" << itr->first << ", " << itr->second << ")";
    auto titr = itr;
    if (++titr != mp.end()) os << " ";
  }
  return os;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const unordered_map<T1, T2> &mp) {
  for (auto itr = mp.begin(); itr != mp.end(); ++itr) {
    os << "(" << itr->first << ", " << itr->second << ")";
    auto titr = itr;
    if (++titr != mp.end()) os << " ";
  }
  return os;
}
using ll = long long int;
using P = pair<int, int>;
const int inf = 1e9;
const ll linf = 1LL << 50;
const double EPS = 1e-10;
const int mod = 1000000007;
const int dx[4] = {-1, 0, 1, 0};
const int dy[4] = {0, -1, 0, 1};
struct fast_io {
  fast_io() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(20);
  }
} fast_io_;
template <typename Monoid>
class LazySegmentTree {
 public:
  using T = typename Monoid::value_type;
  using E = typename Monoid::lazy_type;
  int n;
  T identity;
  E lazy_def;
  vector<T> val;
  vector<E> lazy;
  LazySegmentTree() {}
  LazySegmentTree(int n_, vector<T> v = vector<T>()) {
    identity = Monoid::identity;
    lazy_def = Monoid::lazy_def;
    n = 1;
    while (n < n_) n *= 2;
    val.assign(2 * n - 1, identity);
    lazy.assign(2 * n - 1, lazy_def);
    for (size_t i = 0; i < v.size(); i++) {
      val[i + n - 1] = v[i];
    }
    for (int i = n - 2; i >= 0; i--) {
      val[i] = Monoid::operation(val[2 * i + 1], val[2 * i + 2]);
    }
  }
  void eval(int k, int len) {
    if (lazy[k] == lazy_def) return;
    if (k < n - 1) {
      lazy[2 * k + 1] = Monoid::lazy_accumulate(lazy[2 * k + 1], lazy[k]);
      lazy[2 * k + 2] = Monoid::lazy_accumulate(lazy[2 * k + 2], lazy[k]);
    }
    val[k] = Monoid::lazy_update(val[k], lazy[k], len);
    lazy[k] = lazy_def;
  }
  T update(int a, int b, E &e, int k, int l, int r) {
    eval(k, r - l);
    if (r <= a || b <= l)
      return val[k];
    else if (a <= l && r <= b) {
      lazy[k] = Monoid::lazy_accumulate(lazy[k], e);
      eval(k, r - l);
      return val[k];
    } else {
      T lv = update(a, b, e, 2 * k + 1, l, (l + r) / 2);
      T rv = update(a, b, e, 2 * k + 2, (l + r) / 2, r);
      return val[k] = Monoid::operation(lv, rv);
    }
  }
  T update(int a, int b, E e) { return update(a, b, e, 0, 0, n); }
  T query(int a, int b, int k, int l, int r) {
    eval(k, r - l);
    if (r <= a || b <= l) return identity;
    if (a <= l && r <= b) return val[k];
    T lv = query(a, b, 2 * k + 1, l, (l + r) / 2);
    T rv = query(a, b, 2 * k + 2, (l + r) / 2, r);
    return Monoid::operation(lv, rv);
  }
  T query(int a, int b) { return query(a, b, 0, 0, n); }
  T get(int i) { return query(i, i + 1); }
};
template <typename T, typename E>
class RSQRUQ {
 public:
  using value_type = T;
  using lazy_type = E;
  const static T identity;
  const static E lazy_def;
  RSQRUQ() {}
  static T operation(T &l, T &r) { return l + r; }
  static E lazy_accumulate(E &l, E &r) { return r; }
  static T lazy_update(T &t, E &e, int len) { return e * len; }
};
template <typename T, typename E>
const T RSQRUQ<T, E>::identity = 0;
template <typename T, typename E>
const E RSQRUQ<T, E>::lazy_def = numeric_limits<E>::min();
int main(int argc, char const *argv[]) {
  int n;
  cin >> n;
  ll x;
  cin >> x;
  vector<ll> a(n);
  cin >> a;
  vector<int> e(n);
  for (int i = (0); i < (n); ++i) e[i] = i;
  sort((e).begin(), (e).end(), [&](int i, int j) {
    if (a[i] != a[j]) return a[i] < a[j];
    return i < j;
  });
  ll res = linf;
  for (int t = 0; t < n; t++) {
    ll tmp = (ll)t * x;
    LazySegmentTree<RSQRUQ<ll, ll>> seg(n, vector<ll>(n, 1));
    for (int i_ = (0); i_ < (n); ++i_) {
      int i = e[i_];
      ll r = 0;
      r += seg.query(i, min(n, i + t + 1));
      if (i + t >= n) r += seg.query(0, i + t + 1 - n);
      tmp += a[i] * r;
      seg.update(i, min(n, i + t + 1), 0);
      if (i + t >= n) seg.update(0, i + t + 1 - n, 0);
    }
    chmin(res, tmp);
  }
  cout << res << endl;
  return 0;
}
