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;
const int N = 2 * 1000 + 5;
vector<int> a;
int n, x;
int dp[N][N];
int main() {
  cin >> n >> x;
  for (int i = 0; i < n; i++) {
    int tmp;
    cin >> tmp;
    a.push_back(tmp);
  }
  int ans = 1000 * 1000 * 1000;
  for (int i = 0; i < n; i++) dp[0][i] = a[i];
  for (int i = 1; i < n; i++) {
    for (int j = 0; j < n; j++) {
      dp[i][j] = min(a[((j - i) + n) % n], dp[(i - 1 + n) % n][j]);
    }
  }
  for (int i = 0; i < n; i++) {
    int tmp = 0;
    for (int j = 0; j < n; j++) {
      tmp += dp[i][j];
    }
    ans = min(ans, i * x + tmp);
  }
  cout << ans << endl;
}
