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 a[2000];
int dp[2000][2000];
long long int dp2[2000];
int main() {
  int n, x, i, j;
  scanf("%d%d", &n, &x);
  for (i = 0; i < n; i++) {
    scanf("%d", a + i);
    dp2[0] += dp[i][0] = a[i];
  }
  for (j = 1; j < n; j++) {
    dp2[j] = j * x;
    for (i = 0; i < n; i++) {
      dp2[j] += dp[i][j] =
          ((dp[i][j - 1]) < (a[(i + n - j) % n]) ? (dp[i][j - 1])
                                                 : (a[(i + n - j) % n]));
    }
    dp2[j] = ((dp2[j - 1]) < (dp2[j]) ? (dp2[j - 1]) : (dp2[j]));
  }
  printf("%lld\n", dp2[n - 1]);
  return 0;
}
