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>
template <typename T>
void fin(T const& t) {
  std::cout << t << std::endl;
  exit(0);
}
int main() {
  std::cin.tie(0);
  std::ios::sync_with_stdio(false);
  int N, x;
  std::cin >> N >> x;
  std::vector<int> a(N);
  int mi = 1e9 + 1, p = -1;
  for (int i = 0; i < N; ++i) {
    std::cin >> a[i];
    if (mi > a[i]) {
      mi = a[i];
      p = i;
    }
  }
  auto chmin = [](int& x, int y) {
    if (x > y) x = y;
  };
  for (int i = 1; i < N; ++i) chmin(a[(p + i) % N], a[(p + i - 1) % N] + x);
  int64_t ans = 0;
  for (int i : a) ans += i;
  fin(ans);
  return 0;
}
