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 ll = long long;
using pii = pair<int, int>;
int N, x;
int a[2010];
ll calc(int i, int j) { return a[j] + (i - j + N) % N * (ll)x; }
int main() {
  cin.tie(0);
  ios_base::sync_with_stdio(false);
  cout << fixed << setprecision(10);
  cin >> N >> x;
  for (int i = 0; i < N; i++) {
    cin >> a[i];
  }
  int len = 0;
  ll ans = 0;
  for (int i = 0; i < N; i++) {
    int idx = 0;
    for (int j = 0; j < N; j++) {
      if (calc(i, j) < calc(i, idx)) idx = j;
    }
    len = max(len, (idx - i + N) % N);
    ans += a[idx];
  }
  ans += (ll)x * len;
  cout << ans << endl;
  return 0;
}
