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 Power(long long a, long long b) {
  long long result = 1;
  while (b) {
    if (b % 2) {
      result = (result * a) % 1000000007;
    }
    b = b >> 1;
    a = (a * a) % 1000000007;
  }
  return result;
}
int main() {
  long long N, i, j;
  cin >> N;
  long long x;
  cin >> x;
  vector<long long> V(N);
  for (i = 0; i < N; i++) {
    cin >> V[i];
  }
  long long Sum = 0, Max = 0;
  for (i = 0; i < N; i++) {
    long long Min = V[i], Store = 0;
    for (j = 0; j < N; j++) {
      if (i != j) {
        long long z = (j - i + N) % N;
        if (Min > max(-Max + z, 0LL) * x + V[j]) {
          Store = z;
          Min = max(+z - Max, 0LL) * x + V[j];
        }
      }
    }
    Max = max(Max, Store);
    Sum += Min;
  }
  cout << Sum;
  return 0;
}
