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>
long long signed int n, x, a[2000];
long long signed int min_v[2000][2000], min_i[2000][2000];
int main() {
  scanf("%lld%lld", &n, &x);
  for (int i = (0); i < (n); i++) {
    scanf("%lld", &a[i]);
  }
  for (int i = (0); i < (n); i++) {
    min_v[i][0] = a[i];
    min_i[i][0] = i;
    for (int j = (1); j < (n); j++) {
      int k = (n + (i - j)) % n;
      int v = a[k] + j * x;
      if (min_v[i][j - 1] > v) {
        min_v[i][j] = v;
        min_i[i][j] = k;
      } else {
        min_v[i][j] = min_v[i][j - 1];
        min_i[i][j] = min_i[i][j - 1];
      }
    }
  }
  long long signed int ans = 2000000000001;
  for (int j = (0); j < (n); j++) {
    long long signed int sum = 0;
    for (int i = (0); i < (n); i++) {
      sum += a[min_i[i][j]];
    }
    sum += j * x;
    if (sum < ans) {
      ans = sum;
    }
  }
  printf("%lld\n", ans);
  return 0;
}
