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;
using namespace std;
int main() {
  long long n, x;
  cin >> n >> x;
  vector<long long> a(n);
  for (long long i = 0; i < (n); i++) cin >> a[i];
  vector<vector<long long> > mncost(n,
                                    vector<long long>(n, (long long)1 << 62));
  for (long long i = 0; i < (n); i++) {
    for (long long j = 0; j < (n); j++) {
      mncost[i][j] = min(mncost[i][j], a[(i - j + n) % n] + x * j);
    }
  }
  long long mxj = 0;
  vector<long long> mn(n, 1 << 30);
  for (long long i = 0; i < (n); i++) {
    for (long long j = 0; j < (n); j++) {
      if (mn[i] > mncost[i][j]) {
        mn[i] = mncost[i][j];
        if (mxj < j) mxj = j;
        mn[i] -= x * j;
      }
    }
  }
  long long sum = 0;
  for (long long i = 0; i < (n); i++) sum += mn[i];
  cout << sum + x * mxj << endl;
}
