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, x;
  scanf("%d%d", &n, &x);
  int cnt = 0;
  long long ans = 0ll;
  int mi = INT_MAX;
  for (int i = (0); i < (n); i++) {
    int t;
    scanf("%d", &t);
    mi = min(mi, t);
    if (t <= x) {
      cnt++;
      ans += t;
    }
  }
  if (n == 1) {
    printf("%d\n", mi);
  } else {
    if (cnt) {
      cnt--;
      ans -= mi;
      long long temp = (n - cnt) * mi + (n - cnt - 1) * x;
      ans += temp;
    } else {
      ans = (n * mi) + (n - 1) * x;
    }
    printf("%lld\n", ans);
  }
  return 0;
}
