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;
static const int INTINF = (INT_MAX >> 1);
static const long long LLINF = (LLONG_MAX >> 1);
static const int MAX = 1e5 + 1;
static const long long MOD = 1e9 + 7;
template <class T>
inline bool chmax(T& a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
inline bool chmin(T& a, T b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <typename T>
using min_priority_queue = priority_queue<T, vector<T>, greater<T> >;
string to_string(string s) { return '"' + s + '"'; }
string to_string(bool b) { return b ? "true" : "false"; }
template <size_t N>
string to_string(bitset<N> bs) {
  string res;
  for (size_t i = 0; i < N; ++i) res += '0' + bs[i];
  return res;
}
string to_string(vector<bool> v) {
  string res = "{";
  for (bool e : v) res += to_string(e) + ", ";
  return res += "}";
}
template <class T, class U>
string to_string(pair<T, U> p);
template <class C>
string to_string(C c) {
  string res = "{";
  for (auto e : c) res += to_string(e) + ", ";
  return res += "}";
}
template <class T, class U>
string to_string(pair<T, U> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
void debug() { cerr << '\n'; }
template <class Head, class... Tail>
void debug(Head head, Tail... tail) {
  cerr << '\t' << to_string(head), debug(tail...);
}
int main(int argc, const char* argv[]) {
  std::cout << std::fixed << std::setprecision(15);
  int N;
  cin >> N;
  long long x;
  cin >> x;
  vector<long long> A(N);
  for (int i = 0; i < (N); ++i) {
    cin >> A[i];
  }
  vector<long long> idxs(N);
  long long ma_cnt = 0;
  for (int i = 0; i < (N); ++i) {
    long long k = 0;
    long long mi = LLINF;
    while (k < N) {
      long long tmp = k * x;
      long long idx = i - k;
      if (idx < 0) idx += N;
      tmp += A[idx];
      if (tmp < mi) {
        mi = tmp;
        idxs[i] = idx;
        ma_cnt = max(ma_cnt, k);
      }
      k++;
    }
  }
  long long ans = ma_cnt * x;
  for (int i = 0; i < (N); ++i) {
    ans += A[idxs[i]];
  }
  cout << ans << endl;
  return 0;
}
