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 Vec = 4;
const int Vecy[Vec] = {0, -1, 0, 1};
const int Vecx[Vec] = {1, 0, -1, 0};
const int Modd = 1000000007;
long long dp[2000][2000];
int main() {
  int n;
  long long x;
  long long ans = 10000000000;
  cin >> n >> x;
  for (int i = 0; i < n; i++) {
    cin >> dp[0][i];
  }
  for (int iy = 1; iy < n; iy++) {
    for (int ix = 0; ix < n; ix++) {
      int k;
      if (iy > ix) {
        k = n - (iy - ix);
      } else {
        k = ix - iy;
      }
      dp[iy][ix] = min(dp[iy - 1][ix], dp[0][k]);
    }
  }
  for (int iy = 0; iy < n; iy++) {
    ans = min(ans, accumulate(dp[iy], dp[iy] + n, (long long)0) + x * iy);
  }
  cout << ans << endl;
  return 0;
}
