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 inf = 1 << 28;
const long long INF = 1ll << 50;
const double pi = acos(-1);
const double eps = 1e-8;
const int mod = 1e9 + 7;
const vector<int> emp;
const int dx[4] = {-1, 0, 1, 0}, dy[4] = {0, 1, 0, -1};
const int DX[8] = {-1, -1, -1, 0, 0, 1, 1, 1},
          DY[8] = {1, 0, -1, 1, -1, 1, 0, -1};
int n, x;
vector<int> a;
int main() {
  cin >> n >> x;
  int sum = 0;
  a = vector<int>(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    sum += a[i];
  }
  long long ans = sum;
  vector<vector<int> > dp(n, vector<int>(n));
  dp[0] = a;
  for (int i = 1; i < n; i++) {
    long long res = i * x;
    for (int j = 0; j < n; j++) {
      res += dp[i][j] = min(dp[i - 1][j], a[(j - i + n) % n]);
    }
    ans = min(ans, res);
  }
  cout << ans << endl;
}
