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 Int = long long;
using _int = int;
using ll = long long;
using Double = long double;
const Int INF = (1LL << 60) + 1e9;
const Int mod = (1e9) + 7;
const Double EPS = 1e-8;
const Double PI = 6.0 * asin((Double)0.5);
using P = pair<Int, Int>;
template <class T>
T Max(T& a, T b) {
  return a = max(a, b);
}
template <class T>
T Min(T& a, T b) {
  return a = min(a, b);
}
template <class T1, class T2>
ostream& operator<<(ostream& o, pair<T1, T2> p) {
  return o << "(" << p.first << "," << p.second << ")";
}
template <class T1, class T2, class T3>
ostream& operator<<(ostream& o, tuple<T1, T2, T3> t) {
  return o << "(" << get<0>(t) << "," << get<1>(t) << "," << get<2>(t) << ")";
}
template <class T1, class T2>
istream& operator>>(istream& i, pair<T1, T2>& p) {
  return i >> p.first >> p.second;
}
template <class T>
ostream& operator<<(ostream& o, vector<T> a) {
  Int i = 0;
  for (T t : a) o << (i++ ? " " : "") << t;
  return o;
}
template <class T>
istream& operator>>(istream& i, vector<T>& a) {
  for (T& t : a) i >> t;
  return i;
}
signed main() {
  srand((unsigned)time(NULL));
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  cout << fixed << setprecision(12);
  Int N, x;
  cin >> N >> x;
  vector<Int> A(N);
  cin >> A;
  vector<P> B(N);
  for (int i = 0; i < N; i++) B[i] = P(A[i], i);
  sort(B.begin(), B.end());
  int start = B[0].second;
  Int ans = 0;
  Int mn = INF;
  for (Int i = 0; i < N; i++) {
    int a = mn;
    int b = A[(start + i) % N];
    ans += min(a, b);
    if (a > b) mn = b + x;
  }
  cout << ans << endl;
  return 0;
}
