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() {
  long long n, x;
  cin >> n >> x;
  long long a[2002];
  for (long long i = (long long)(0); i < (long long)(n); i++) {
    cin >> a[i];
  }
  long long mq[2002];
  for (long long i = (long long)(0); i < (long long)(n); i++) {
    mq[i] = a[i];
  }
  long long m = INT_MAX / 3;
  for (long long k = (long long)(0); k < (long long)(n); k++) {
    long long s = 0;
    for (long long i = (long long)(0); i < (long long)(n); i++) {
      mq[i] = (mq[i] < a[(i - k) % n >= 0 ? (i - k) % n : (i - k) % n + n]
                   ? mq[i]
                   : a[(i - k) % n >= 0 ? (i - k) % n : (i - k) % n + n]);
      s += mq[i];
    }
    m = (m < k * x + s ? m : k * x + s);
  }
  cout << m << endl;
  return 0;
}
