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>
const int MAX_N = 2050;
int N;
long long x, a[MAX_N];
struct Method {
  int base;
};
Method best[MAX_N];
long long cal_time(int mn) {
  long long ret = 0;
  for (int i = 0; i < N; i++) {
    ret += a[best[i].base];
  }
  return ret + x * mn;
}
int main(int argc, char **argv) {
  std::cin >> N >> x;
  for (int i = 0; i < N; i++) {
    std::cin >> a[i];
  }
  long long ret = 0;
  for (int i = 0; i < N; i++) {
    best[i].base = i;
    ret += a[i];
  }
  for (int mn = 1; mn < N; mn++) {
    for (int i = 0; i < N; i++) {
      int prev = (i - 1 + N) % N;
      if (a[best[prev].base] < a[i]) {
        best[i].base = best[prev].base;
      }
    }
    ret = std::min(ret, cal_time(mn));
  }
  std::cout << ret << std::endl;
  return 0;
}
