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;
const int xx[] = {0, 1, 0, -1, -1, 1, -1, 1};
const int yy[] = {1, 0, -1, 0, 1, 1, -1, -1};
const int kx[] = {-2, -1, 1, 2, 2, 1, -1, -2};
const int ky[] = {1, 2, 2, 1, -1, -2, -2, -1};
long long int arr[2005];
int main() {
  int i, j, k, x, n, mn, idx;
  long long int sum, ans = 0;
  scanf("%d%d", &n, &x);
  mn = INT_MAX;
  sum = ans;
  for (i = 1; i <= n; i++) {
    scanf("%lld", &arr[i]);
    if (mn >= arr[i]) {
      mn = arr[i];
      idx = i;
    }
    sum += arr[i];
  }
  ans = (mn * n) + (1LL * x * (n - 1));
  printf("%lld\n", min(sum, ans));
  return 0;
}
