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>
using namespace std;
long long a[40010];
long long q[40010];
int l, r;
int main() {
  int n;
  long long x;
  cin >> n >> x;
  for (int i = 1; i <= n; i++) {
    scanf("%lld", &a[i]);
  }
  for (int i = n + 1; i <= n + n; i++) a[i] = a[i - n];
  long long lastans = 1e18;
  for (int xx = 0; xx <= n; xx++) {
    l = 1;
    r = 0;
    long long ans = 0;
    for (int i = n + 1 - xx; i <= n; i++) {
      while (r >= l && a[i] <= q[r]) r--;
      q[++r] = i;
    }
    for (int i = n + 1; i <= n + n; i++) {
      while (l <= r && q[l] < i - xx) l++;
      while (r >= l && a[i] <= a[q[r]]) r--;
      q[++r] = i;
      ans += a[q[l]];
    }
    if (lastans > ans + (long long)xx * x) lastans = ans + (long long)xx * x;
  }
  cout << lastans;
}
