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 <class T>
using vec = vector<T>;
template <typename Iter>
ostream &_IterOutput_(ostream &o, Iter b, Iter e, const string ss = "",
                      const string se = "") {
  o << ss;
  for (auto it = b; it != e; it++) o << (it == b ? "" : ", ") << *it;
  return o << se;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &o, const pair<T1, T2> &pair) {
  return o << "(" << pair.first << ", " << pair.second << ")";
}
template <typename T>
ostream &operator<<(ostream &o, const vector<T> &vec) {
  return _IterOutput_(o, begin(vec), end(vec), "[", "]");
}
template <typename T>
ostream &operator<<(ostream &o, const set<T> &st) {
  return _IterOutput_(o, begin(st), end(st), "{", "}");
}
template <typename T, size_t N>
ostream &operator<<(ostream &o, const array<T, N> &arr) {
  return _IterOutput_(o, begin(arr), end(arr), "|", "|");
}
template <typename T1, typename T2>
ostream &operator<<(ostream &o, const map<T1, T2> &mp) {
  o << "{";
  for (auto it = mp.begin(); it != mp.end(); it++) {
    o << (it == mp.begin() ? "" : ", ") << it->first << ":" << it->second;
  }
  o << "}";
  return o;
}
const long long MX = 2222;
long long N, X;
long long ip[MX];
long long op[MX];
int32_t main() {
  do {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
  } while (0);
  cin >> N >> X;
  for (long long i = 0; i < N; i++) {
    cin >> ip[i];
    op[i] = ip[i];
  }
  const long long INF = 1e18;
  long long ans = INF;
  for (long long i = 0; i <= N; i++) {
    long long z = 0;
    for (long long j = 0; j < N; j++) {
      z += op[j];
    }
    ans = min(ans, z + i * X);
    for (long long j = 0; j < N; j++) {
      long long t = (j + N + N - i - 1) % N;
      op[j] = min(op[j], op[t]);
    }
  }
  cout << ans << endl;
  return 0;
}
