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(int argc, char* argv[]) {
  int N;
  long int x;
  scanf("%d %ld", &N, &x);
  long int a[N];
  int i, n;
  for (i = 0; i < N; ++i) {
    scanf("%ld", &a[i]);
  }
  long int ans = 0;
  for (n = 0; n < N; ++n) {
    ans += a[n];
  }
  int subans;
  for (i = 1; i < N; ++i) {
    if (a[N - 1] > a[0]) {
      a[N - 1] = a[0];
    }
    subans = a[N - 1];
    for (n = N - 1; n > 0; --n) {
      if (a[n - 1] > a[n]) {
        a[n - 1] = a[n];
      }
      subans += a[n - 1];
    }
    subans += x * i;
    if (subans < ans) {
      ans = subans;
    }
  }
  printf("%ld\n", ans);
  return 0;
}
