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(void) {
  int min[2000][2000];
  int a[2000];
  int N, x;
  long long sum, summin;
  int i, j, k;
  scanf("%d%d", &N, &x);
  for (i = 0; i < N; i++) scanf("%d", &a[i]);
  for (i = 0; i < N; i++) {
    min[0][i] = a[i];
    sum += a[i];
  }
  summin = sum;
  for (i = 1; i < N; i++) {
    sum = 0;
    for (j = 0; j < N; j++) {
      k = (j - i >= 0) ? j - i : N + j - i;
      min[i][j] = (((min[i - 1][j]) < (a[k])) ? (min[i - 1][j]) : (a[k]));
      sum += min[i][j];
    }
    sum += i * x;
    if (sum < summin) summin = sum;
  }
  printf("%lld\n", summin);
  return 0;
}
