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;
using ld = long double;
ll INF = LLONG_MAX;
using vi = vector<int>;
using vll = vector<ll>;
using pii = pair<int, int>;
namespace output {
void pr(int x) { cout << x; }
void pr(long x) { cout << x; }
void pr(ll x) { cout << x; }
void pr(unsigned x) { cout << x; }
void pr(unsigned long x) { cout << x; }
void pr(unsigned long long x) { cout << x; }
void pr(float x) { cout << x; }
void pr(double x) { cout << x; }
void pr(ld x) { cout << x; }
void pr(char x) { cout << x; }
void pr(const char* x) { cout << x; }
void pr(const string& x) { cout << x; }
void pr(bool x) { pr(x ? "true" : "false"); }
template <class T>
void pr(const complex<T>& x) {
  cout << x;
}
template <class T1, class T2>
void pr(const pair<T1, T2>& x);
template <class T>
void pr(const T& x);
template <class T, class... Ts>
void pr(const T& t, const Ts&... ts) {
  pr(t);
  pr(ts...);
}
template <class T1, class T2>
void pr(const pair<T1, T2>& x) {
  pr("{", x.f, ", ", x.s, "}");
}
template <class T>
void pr(const T& x) {
  pr("{");
  bool fst = 1;
  for (const auto& a : x) pr(!fst ? ", " : "", a), fst = 0;
  pr("}");
}
void print() { pr("\n"); }
template <class T, class... Ts>
void print(const T& t, const Ts&... ts) {
  pr(t);
  if (sizeof...(ts)) pr(" ");
  print(ts...);
}
}  // namespace output
using namespace output;
int main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int N, x;
  cin >> N >> x;
  vi arr(N);
  for (int i = (0); i < (N); ++i) cin >> arr[i];
  ll ans = 0;
  int rots = 0;
  for (int i = (0); i < (N); ++i) {
    ll best = arr[i];
    int c = arr[i];
    for (int j = (0); j < (N); ++j) {
      if (1LL * x * j + arr[(i - j + N) % N] < best) {
        rots = max(rots, j);
        best = 1LL * x * j + arr[(i - j + N) % N];
        c = arr[(i - j + N) % N];
      }
    }
    ans += c;
  }
  print(ans + 1LL * x * rots);
}
