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>
static const auto NMAX = 2000;
static int N, X, A[NMAX];
static int64_t solve(int L) {
  int64_t ret = 0;
  for (auto i = 0; i < N; i++) {
    auto m = A[i];
    for (auto j = 1, k = i; j <= L; j++) {
      if (++k == N) k = 0;
      m = std::min(m, A[k]);
    }
    ret += m;
  }
  return ret;
}
int main() {
  std::ios_base::sync_with_stdio(false);
  std::cin >> N >> X;
  for (auto i = 0; i < N; i++) std::cin >> A[i];
  auto s = solve(0);
  for (auto i = 1; i < N; i++) s = std::min(s, (int64_t)X * i + solve(i));
  std::cout << s << std::endl;
  return 0;
}
