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 <iostream>
#include <string>
#include <algorithm>
#include <vector>
#include <cassert>
#include <map>
using namespace std;

int main() {
  std::ios_base::sync_with_stdio(false);
  cin.tie(0);
  int n, x;
  cin >> n >> x;
  std::vector<int> v(n);
  for (auto& el : v) {
    cin >> el;
  }

  auto ind = std::min_element(v.begin(), v.end()) - v.begin();
  int64_t ans = (int64_t)1e18;
  for (int k = 0; k < n; k++) {
    auto begin_seg = ind;
    auto cur = ind;
    auto sum = 0LL;
    int can_take = k;
    for (int i = 0; i < n; i++) {
      if (v[begin_seg] >= v[cur]) {
        begin_seg = cur;
        can_take = k;
      }
      sum += v[begin_seg];
      cur++;
      cur %= n;
      if (can_take == 0) {
        can_take = k;
        begin_seg = cur;
      } else {
        can_take--;
      }
    }
    ans = min(ans, sum + x * 1ll * k);

  }

  cout << ans << endl;




  return 0;
}