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 MAXN = 1e5 + 17;
long long a[MAXN], b[MAXN];
int main(int argc, char const *argv[]) {
  int n;
  long long x;
  cin >> n >> x;
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
    b[i] = 0x3fffffffffffffff;
  }
  int mx = 0;
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < i; ++j) {
      if (a[j] + (i - j) * x <= a[i])
        b[i] = min(b[i], a[j]), mx = max(mx, i - j);
    }
    for (int j = i + 1; j < n; ++j) {
      if (a[j] + (j - i + n - 2) * x <= a[i])
        b[i] = min(b[i], a[j]), mx = max(mx, j - i + n - 2);
    }
  }
  long long ans = 0;
  for (int i = 0; i < n; ++i) {
    if (b[i] == 0x3fffffffffffffff)
      ans += a[i];
    else
      ans += b[i];
  }
  ans += mx * x;
  cout << ans << endl;
  return 0;
}
