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;
int main() {
  int n;
  scanf("%d", &n);
  int x;
  scanf("%d", &x);
  vector<int> as(n);
  for (__typeof(n) i = (0) - ((0) < (n) ? 0 : 1);
       i != (n) - ((0) < (n) ? 0 : 1); i += ((0) < (n) ? 1 : -1)) {
    scanf("%d", &as[i]);
  };
  vector<int> dp(n);
  for (__typeof(n) i = (0) - ((0) < (n) ? 0 : 1);
       i != (n) - ((0) < (n) ? 0 : 1); i += ((0) < (n) ? 1 : -1)) {
    dp[i] = as[i];
  }
  unsigned long long ans = -1;
  for (__typeof(n) i = (0) - ((0) < (n) ? 0 : 1);
       i != (n) - ((0) < (n) ? 0 : 1); i += ((0) < (n) ? 1 : -1)) {
    for (__typeof(n) j = (0) - ((0) < (n) ? 0 : 1);
         j != (n) - ((0) < (n) ? 0 : 1); j += ((0) < (n) ? 1 : -1)) {
      dp[j] = min(dp[j], as[(j + n - i) % n]);
    }
    ans = min(ans, accumulate(begin(dp), end(dp), 0ULL) + x * i);
  }
  printf("%llu\n", ans);
  return 0;
}
