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[N];
  for (int i = 0; i < N; i++) cin >> a[i];
  long long totm = 0;
  long long tota = 0;
  for (int i = N - 1; i >= 0; i--) {
    long long mn = a[i];
    long long mna = a[i];
    long long mmul = 0;
    int j = (i - 1 + N) % N;
    long long mul = 1;
    while (j != i) {
      if ((mul > totm ? mul : 0) * X + a[j] < mn) {
        mn = (mul > totm ? mul : 0) * X + a[j];
        mna = a[j];
        mmul = mul;
      }
      mul++;
      j = (j - 1 + N) % N;
    }
    tota += mna;
    totm = max(totm, mmul);
  }
  long long tot = tota + X * totm;
  cout << tot;
  return 0;
}
