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
my ($N, $x) = <STDIN>;
my @a = split(/ /,<STDIN>);
calculate($N, $x, \@a);


sub calculate{
  my $min_val_id = 0;
  my ($N, $x, $a) = @_;

  foreach my $i (0..$N-1){
    $min_val_id = $i if($a->[$min_val_id] > $a->[$i]);
  }

  my $sum_time = 0;
  my $max_changed_count = 0;
  my $changed_count = 0;

  #I shuld be this program refactering
  foreach my $i (0..$N-1){
    my $current_id = ($min_val_id + $i) % $N;
    my $prev_id = ($current_id) ? $current_id-1 : $N-1;
    my $current_time = 0;
    if ($a->[$current_id] <= $x || $a->[$current_id] <= $a->[$prev_id]+$x*($changed_count+1)){
      $current_time = $a->[$current_id];
      $changed_count = 0;
    }else{
      $current_time = $a->[$current_id] = $a->[$prev_id];
      ++$changed_count;
    }
    $sum_time += $current_time;
    $max_changed_count = $changed_count if $changed_count > $max_changed_count;
  }
  $sum_time += $x*$max_changed_count;
  print "$sum_time\n";

}