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 MIN(int a, int b) { return a < b ? a : b; }
int main() {
  int n, m, i, j, d[4010], max, s, k, min = 1e9;
  scanf("%d %d", &n, &m);
  for (i = 0; i < n; i++) scanf("%d", &d[i]);
  for (i = 0; i < n; i++) d[i + n] = d[i];
  for (i = 0; i < n; i++) {
    for (j = max = s = 0; j < n; j += k) {
      for (k = 1; j + k < n; k++) {
        if (d[i + j] + m > d[i + j + k]) break;
      }
      s += d[i + j] * k;
      if (max < k) max = k;
    }
    s += (max - 1) * m;
    if (min > s) min = s;
  }
  printf("%d\n", min);
  return 0;
}
