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() {
  ios_base::sync_with_stdio(false);
  cout << setprecision(12) << fixed;
  int N;
  long long x;
  cin >> N >> x;
  long long A[N];
  for (int i = (0); i < (N); ++i) {
    cin >> A[i];
  }
  long long dp[N + 1][N];
  fill_n(dp[0], N, 0);
  for (int len = (1); len < (N + 1); ++len) {
    for (int start = (0); start < (N); ++start) {
      dp[len][start] = min(dp[len - 1][start] + A[(start + len - 1) % N],
                           A[start] + dp[len - 1][(start + 1) % N]);
    }
    for (int start = (0); start < (N + 1); ++start) {
      dp[len][start % N] =
          min(dp[len][start % N], dp[len][(start - 1 + N) % N] + x);
    }
  }
  long long result = dp[N][0];
  for (int start = (1); start < (N); ++start) {
    result = min(result, dp[N][start]);
  }
  cout << result << endl;
  return 0;
}
