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>
ostream &operator<<(ostream &o, const vector<T> &v) {
  o << "{";
  for (int i = 0; i < (int)v.size(); i++) o << (i > 0 ? ", " : "") << v[i];
  o << "}";
  return o;
}
void solve(void) {
  int N;
  long long x;
  cin >> N >> x;
  vector<long long> as(N);
  for (long long i = 0; i <= N - 1; i++) cin >> as[i];
  long long ans = 0LL, ope = 0LL;
  for (long long i = 0; i <= N - 1; i++) {
    long long tmp = as[i], mos = i, magic = 0;
    for (long long j = 0; j <= N - 1; j++) {
      if (tmp >= as[(i - j + N) % N] + x * j) {
        tmp = as[(i - j + N) % N] + x * j;
        magic = j;
        mos = (i - j + N) % N;
      }
    }
    ope = max(magic, ope);
    ans += as[mos];
  }
  ans += x * ope;
  cout << ans << endl;
}
int main(void) {
  solve();
  return 0;
}
