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;
long long n, m, s[110000], ans = 1999999999999999999;
vector<pair<long long, long long>> p;
vector<long long> v;
int main() {
  cin >> n >> m;
  for (int i = 0; i < n; i++) {
    cin >> s[i];
    p.push_back(make_pair(s[i], i));
  }
  sort(p.begin(), p.end());
  for (int i = 0; i < n; i++) {
    long long now = m * (n - i - 1);
    v.push_back(p[i].second);
    sort(v.begin(), v.end());
    for (int i = 0; i < v.size(); i++) {
      if (i == v.size() - 1)
        now += ((v[0] + n) - v[i]) * s[v[i]];
      else
        now += (v[i + 1] - v[i]) * s[v[i]];
    }
    ans = min(ans, now);
  }
  cout << ans << endl;
}
