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 <iostream>
#define REP(i, a, n) for(int i = a; i < n; i++)
using namespace std;


long N, x, a[2001];

int main(void) {
  cin >> N >> x;
  REP(i, 1, N + 1) cin >> a[i];

  long cost = 0;
  long cnt = 0;

  REP(i, 1, N + 1) {
    long m = a[i];
    long p = a[i];
    REP(j, 1, N) {
      int k = (i - j + N - 1) % N + 1;
      if(a[k] + j * x < m) {
        m = a[k] + j * x;
        p = a[k];
        cnt = max(cnt, j);
      }
    }
    cost += p;
  }

  cost += cnt * x;

  cout << cost << endl;

  return 0;
}
