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 A[4000];
int move_count[4000];
int dp[4000][4000];
int main() {
  int N, x;
  cin >> N >> x;
  for (int i = 0; i < N; i++) cin >> A[i];
  for (int i = 0; i < N; i++)
    for (int j = 0; j < N; j++) dp[i][(i + j) % N] = A[i] + j * x;
  long long ans = 0;
  for (int j = 0; j < N; j++) {
    int mini = -1;
    int k;
    for (int i = 0; i < N; i++)
      if (mini == -1 or mini > dp[i][j]) {
        mini = dp[i][j];
        k = i;
      }
    ans += mini;
    if (j >= k)
      ++move_count[j - k];
    else
      ++move_count[N - (k - j)];
  }
  bool flag = false;
  int num = 0;
  for (int i = N - 1; i >= 0; i--) {
    if (!flag and move_count[i] > 0) {
      flag = true;
      num = (move_count[i] - 1) * i;
    } else if (move_count[i] > 0)
      num += move_count[i] * i;
  }
  ans -= num * x;
  cout << ans << endl;
}
