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 N, x;
int arr[2005][2005];
vector<int> abc;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> N >> x;
  int suma = 0;
  for (int i = 1; i <= N; i++) {
    cin >> arr[0][i];
    suma += arr[0][i];
  }
  arr[0][N + 1] = suma;
  suma = 0;
  for (int vuelta = 1; vuelta < N; vuelta++) {
    suma = arr[vuelta - 1][0] + x;
    arr[vuelta][0] = suma;
    for (int slime = 1; slime <= N; slime++) {
      int temp = (slime + vuelta > N) ? (slime + vuelta) % N : slime + vuelta;
      arr[vuelta][slime] = min(arr[vuelta - 1][slime], arr[0][temp]);
      suma += arr[vuelta][slime];
    }
    arr[vuelta][N + 1] = suma;
  }
  int result = INT_MAX;
  for (int i = 0; i < N; i++) result = min(result, arr[i][N + 1]);
  cout << result << "\n";
  return 0;
}
