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 int64 = long long;
template <class T>
ostream& operator<<(ostream& os, vector<T>& _) {
  os << '{';
  for (T& x : _) {
    os << x;
    if (&x != &_.back()) os << ',';
  }
  os << '}';
  return os;
}
template <class T, class U>
ostream& operator<<(ostream& os, pair<T, U>& p) {
  return os << '{' << p.first << " " << p.second << '}';
}
constexpr int64 INF = 1e18;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  int n;
  int64 x;
  cin >> n >> x;
  vector<int64> a(n);
  for (int i = 0; i < n; ++i) cin >> a[i];
  int magic_cnt = 0;
  int64 sum = 0;
  for (int i = 0; i < n; ++i) {
    int64 cost = INF;
    int cnt = 0;
    for (int j = i; j < i + n; ++j) {
      int pos = j % n;
      int diff = j - i;
      if (a[pos] + diff * x < cost) {
        cost = a[pos] + diff * x;
        cnt = diff;
        magic_cnt = max(magic_cnt, diff);
      }
    }
    sum += cost - x * cnt;
  }
  cout << sum + magic_cnt * x << endl;
  return 0;
}
