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() {
  long long a[2000];
  long long x;
  long long pos_t, num_t;
  long long time = 0;
  int n;
  long long pos, num;
  long long max = 0;
  scanf("%d %lld", &n, &x);
  for (int i = 0; i < n - 1; i++) {
    scanf("%lld ", &a[i]);
  }
  scanf("%lld", &a[n - 1]);
  if (x > 50000000) printf("failed");
  for (int i = 0; i < n; i++) {
    pos = i;
    pos_t = i;
    num = 0;
    num_t = 0;
    while (1) {
      if (pos == 0)
        pos = n - 1;
      else
        pos--;
      num++;
      if (pos == i) {
        break;
      }
      if ((a[pos] + (x * num)) < (a[pos_t] + (x * num_t))) {
        pos_t = pos;
        num_t = num;
      }
    }
    if (num_t > max) max = num_t;
    time += a[pos_t];
  }
  printf("%lld\n", time + (max * x));
  return 0;
}
