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>
auto size(T&& a) -> decltype(a.size(), int()) {
  return a.size();
}
template <class T>
typename make_signed<decltype(T() % 0)>::type size(T a) {
  return a;
}
void Calc();
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin.exceptions(istream::failbit | istream::badbit);
  cout << fixed << setprecision(15);
  Calc();
  cout.flush();
  return 0;
}
template <class A>
void amax(A& a, A b) {
  a = max(a, b);
}
template <class A>
void amin(A& a, A b) {
  a = min(a, b);
}
struct Scanner {
  template <class A = string>
  A Next() {
    A a;
    cin >> a;
    return a;
  }
  template <class A = int>
  vector<A> Array(int n) {
    vector<A> a(n);
    for (A& i : a) cin >> i;
    return a;
  }
  string Line() {
    string s;
    getline(cin, s);
    return s;
  }
  template <class A>
  Scanner& operator,(A& a) {
    a = Next<A>();
    return *this;
  }
  template <class A>
  operator A() {
    return Next<A>();
  }
} in;
void Calc() {
  long long n, x;
  in, n, x;
  auto a = in.Array<long long>(n);
  long long sum = 0;
  for (auto& i : a) {
    sum += i;
  }
  auto it = min_element(begin(a), end(a));
  auto mini = *it;
  const int INF = 1e9 - 1 + 100;
  long long ret = INF;
  for (decltype(size(n)) pos = size(0), _lpos = size(n); pos < _lpos; pos++)
    if (mini == a[pos]) {
      long long ans = 0;
      int num = 0;
      long long pre_num = 0;
      long long now_mini = INF;
      for (decltype(size(n)) j = size(0), _lj = size(n); j < _lj; j++) {
        int i = a[(pos + j) % n];
        if (pre_num) {
          if (now_mini < i)
            if (now_mini < mini + x) {
              ans += now_mini;
              pre_num--;
              continue;
            }
        }
        if (i < mini + x) {
          now_mini = i;
          ans += i;
          pre_num = num;
        } else {
          ans += mini + x;
          num++;
          pre_num = 0;
          now_mini = INF;
        }
      }
      amin(ret, ans);
    }
  cout << (min(ret, sum)) << endl;
}
