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() {
  long long n, x;
  std::cin >> n >> x;
  vector<long long> a(n);
  for (int i = 0; i < n; i++) {
    std::cin >> a[i];
  }
  long long ans = 0;
  for (int i = 0; i < n; i++) {
    long long res = 1e16;
    for (int k = 0; k <= n; k++) {
      res = min(res, a[(i + n - k) % n]);
    }
    ans += res;
  }
  ans += x * n;
  long long l = -1;
  long long r = n;
  while (r - l > 1) {
    long long m = (l + r) / 2;
    long long res2 = 0;
    for (int i = 0; i < n; i++) {
      long long res = 1e18;
      for (int k = 0; k <= m; k++) {
        res = min(res, a[(i + n - k) % n]);
      }
      res2 += res;
    }
    res2 += x * m;
    if (res2 < ans) {
      r = m;
      ans = res2;
    } else {
      l = m;
    }
  }
  std::cout << ans << std::endl;
}
