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, x;
  scanf("%d %d", &N, &x);
  long a[N];
  for (int i = 0; i < N; ++i) {
    scanf("%ld", &a[i]);
  }
  long min_cost[N][N];
  long min_sum = -1;
  for (int k = 0; k < N; ++k) {
    long temp_sum = 0;
    if (k == 0) {
      for (int i = 0; i < N; ++i) {
        min_cost[k][i] = a[i];
        temp_sum += min_cost[k][i];
      }
    } else {
      for (int i = 0; i < N; ++i) {
        int idx = (i - k) % N;
        if (idx < 0) {
          idx = N + idx;
        }
        min_cost[k][i] = min(min_cost[k - 1][i], a[idx]);
        temp_sum += min_cost[k][i];
      }
    }
    if (min_sum == -1) {
      min_sum = k * x + temp_sum;
    } else {
      int temp = k * x + temp_sum;
      if (temp < min_sum) {
        min_sum = temp;
      }
    }
  }
  printf("%ld\n", min_sum);
  return 0;
}
