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 a[2002];
int memo[2002][2002];
int mmm(int i, int n) {
  return (memo[i][n] =
              (n == 1 ? a[i] : min(memo[(i + N - 1) % N][n - 1], a[i])));
}
signed main() {
  cin >> N >> X;
  for (int i = 0; i < N; i++) cin >> a[i];
  int q = 1 << 30;
  for (int t = 0; t < N; t++) {
    int r = 0;
    for (int i = 0; i < N; i++) {
      r += mmm((N + i - t) % N, t + 1);
    }
    q = min(q, r + X * t);
  }
  cout << q << endl;
}
