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>
int main(void) {
  long long N = 0;
  long long x = 0;
  std::cin >> N >> x;
  long long A = 0;
  std::vector<long long> a;
  while (std::cin >> A) {
    a.push_back(A);
  }
  std::vector<long long> cost;
  long long temp = 0;
  for (int k = 0; k < N; k++) {
    for (long long i = 0; i < N; i++) {
      temp = k * x + a[(N + i - k) % N];
      if (k == 0) {
        cost.push_back(temp);
      }
      cost[i] = std::min(temp, cost[i]);
    }
  }
  long long result = 0;
  for (auto ite = cost.begin(); ite != cost.end(); ite++) {
    result = result + *ite;
  }
  std::cout << result << std::endl;
  return 0;
}
