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 long long mod = 1000000007;
int main() {
  int n;
  long long x;
  cin >> n >> x;
  std::vector<long long> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  int mind = 0;
  for (int i = 0; i < n; i++) {
    if (a[i] < a[mind]) mind = i;
  }
  long long INF = 1e18;
  std::vector<long long> d(n);
  for (int i = 0; i < n; i++) {
    d[(mind + i) % n] = ((long long)(i + 1)) * a[mind] + x * (long long)i;
  }
  for (int i = 1; i < n; i++) {
    for (int j = 0; j < n - i; j++) {
      d[(mind + i + j) % n] =
          min(d[(mind + i + j) % n],
              d[(mind + i - 1) % n] + ((long long)(j + 1)) * a[(mind + i) % n] +
                  x * (long long)j);
    }
  }
  cout << d[(mind + n - 1) % n];
}
