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>
using namespace std;
int main() {
  int N;
  int x;
  cin >> N >> x;
  int a[4016];
  for (int i = 0; i < N; ++i) {
    cin >> a[i];
    a[N + i] = a[i];
  }
  int nextMin[4016];
  for (int i = 0; i < 2 * N; ++i) {
    int c = i + 1;
    while (c < 2 * N && a[c] >= a[i]) {
      ++c;
    }
    if (c == 2 * N) {
      nextMin[i] = i;
    } else {
      nextMin[i] = c;
    }
  }
  unsigned long long int ans = (unsigned long long int)1e9 * 1e9;
  for (int i = 0; i < N; ++i) {
    unsigned long long int cur_ans = x * i;
    int cur_min = 0;
    for (int j = 0; j < N; ++j) {
      if (cur_min < j) {
        cur_min = j;
      }
      if (nextMin[cur_min] != cur_min && nextMin[cur_min] <= j + i) {
        cur_min = nextMin[cur_min];
      }
      cur_ans += a[cur_min];
    }
    ans = min(ans, cur_ans);
  }
  cout << ans << "\n";
  return 0;
}
