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;
struct P {
  long long d;
  int id;
  int root;
  bool operator>(const P &p) const { return d > p.d; }
};
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int n;
  long long x;
  cin >> n >> x;
  vector<long long> a(n);
  vector<bool> memo(n, false);
  priority_queue<P, vector<P>, greater<P> > pq;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    pq.push((P){a[i], i, i});
  }
  long long ans = 0;
  int magic = 0;
  while (!pq.empty()) {
    P tar = pq.top();
    pq.pop();
    if (memo[tar.id] || tar.d > a[tar.id]) continue;
    memo[tar.id] = true;
    a[tar.id] = tar.d;
    ans += a[tar.root];
    magic = max(magic, (tar.id - tar.root + n) % n);
    long long tmp = tar.d + x;
    int idx = (tar.id + 1) % n;
    if (!memo[idx] && tmp < a[idx]) pq.push((P){tmp, idx, tar.root});
  }
  ans += magic * x;
  cout << ans << "\n";
  return 0;
}
