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);
  int64_t ans = 0;
  for (int i = 0; i < N; ++i) {
    std::cin >> a[i];
    ans += a[i];
  }
  for (int64_t k = 1; k < N; ++k) {
    int64_t cur = k * x;
    if (cur >= ans) continue;
    int save = a[N - 1];
    for (int i = 0; i < N - 1; ++i) a[i + 1] = std::min(a[i], a[i + 1]);
    a[0] = std::min(a[0], save);
    for (int i : a) cur += i;
    ans = std::min(ans, cur);
  }
  fin(ans);
  return 0;
}
