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;
int main() {
  int n;
  long long x;
  cin >> n >> x;
  long long a[n];
  for (int((i)) = (0); ((i)) < ((n)); ((i))++) cin >> a[i];
  pair<long long, long long> dp[n];
  for (int((i)) = (0); ((i)) < ((n)); ((i))++)
    dp[i] = pair<long long, long long>(1e17, 1e17);
  for (int((i)) = (0); ((i)) < ((n)); ((i))++) {
    if (dp[i].first > a[i]) dp[i] = pair<long long, long long>(a[i], 0);
    for (int((j)) = (0); ((j)) < ((n - 1)); ((j))++) {
      int k = (i + j) % n;
      if (dp[k].first + x < dp[(k + 1) % n].first)
        dp[(k + 1) % n] =
            pair<long long, long long>(dp[k].first + x, dp[k].second + 1);
    }
  }
  long long ans = 0;
  int cnt = 0;
  for (int((i)) = (0); ((i)) < ((n)); ((i))++) {
    ans += a[(i - dp[i].second + n) % n];
    if (cnt < dp[i].second) cnt = dp[i].second;
  }
  cout << ans + cnt * x << endl;
}
