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;
long long n, a[3000], x, sum, minx = 99999999999999999LL,
                              mx = 999999999999999999LL, mpos = 0;
long long solve(int r) {
  vector<long long> vec1(n + 1, 0);
  vector<long long> A;
  for (int i = mpos; i < mpos + n; i++) A.push_back(a[i % n]);
  A.push_back(0);
  vec1[0] = 0;
  for (int i = 1; i <= n; i++) {
    vec1[i] = vec1[max(0, i - r - 1)] + A[max(0, i - r - 1)] * (r + 1);
  }
  return vec1[n];
}
int main() {
  cin >> n >> x;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    if (mx > a[i]) {
      mx = a[i];
      mpos = i;
    }
  }
  for (int i = 0; i < n; i++) {
    minx = min(minx, solve(i) + i * x);
  }
  cout << minx << endl;
  return 0;
}
