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 n, i, j, a[2222], min[2222][2222], ans, x, p;
  scanf("%ld%ld", &n, &x);
  for (i = 0; i < n; i++) scanf("%ld", &a[i]);
  for (i = 0; i < n; i++)
    for (j = 0; j < n; j++) min[i][j] = 100000000000;
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      if (a[(i - j) % n] < min[i][(i - j + 1) % n])
        min[i][(i - j) % n] = a[(i - j) % n];
      else
        min[i][(i - j) % n] = min[i][(i - j + 1) % n];
    }
  }
  ans = 10000000000000;
  for (i = 0; i < n; i++) {
    p = 0;
    for (j = 0; j < n; j++) p += min[i][(i - j) % n];
    p += j * x;
    if (p < ans) ans = p;
  }
  printf("%ld\n", ans);
  return 0;
}
