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>
void chmin(T& a, T b) {
  a = min(a, b);
}
template <class T>
void chmax(T& a, T b) {
  a = max(a, b);
}
constexpr int INF = 1 << 30;
constexpr long long INFL = 1LL << 60;
constexpr long long MOD = 1000000007;
constexpr long double EPS = 1e-12;
long double PI = acos(-1.0);
void solve() {
  long long n, x;
  cin >> n >> x;
  vector<long long> a(n);
  for (long long i = 0; i < n; i++) cin >> a[i];
  long long ans = 0;
  long long max_diff = 0;
  for (long long i = 0; i < n; i++) {
    long long _max_diff = n;
    long long _ans = 0;
    long long add = INFL;
    for (long long j = 0; j < n; j++) {
      long long diff = i - j;
      if (diff < 0) diff += n;
      long long _add = a[j] + diff * x;
      if (add > _add || (add == _add && _max_diff > diff)) {
        _max_diff = diff;
        add = _add;
        _ans = a[j];
      }
    }
    chmax(max_diff, _max_diff);
    ans += _ans;
  }
  ans += max_diff * x;
  cout << ans << endl;
  return;
}
int main() {
  std::cin.tie(nullptr);
  std::ios_base::sync_with_stdio(false);
  cout << fixed << setprecision(15);
  solve();
}
