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
use strict;
use warnings;
use utf8;
use Data::Dumper;

use constant SUMPLE_DATA =>
[
  +{ input => ["2 10\n", "1 100\n"], answer => 12 },
  +{ input => ["3 10\n", "100 1 100\n"], answer => 23 },
  +{ input => ["4 10\n", "1 2 3 4\n"], answer => 10 },
];

use strict;
use warnings;
use utf8;

my $sum;


my ($N, $x) = split(/ /, stdin());
my @a = split(/ /, stdin());
$sum = func($N, $x, \@a);
print "$sum\n";

sub stdin{
  my $inputs  = <STDIN>;
  chomp($inputs);
  $inputs;
}

sub func{
  my ($data_size, $x, $data) = @_;
  my $min_sum = 0xffff;
  my $ary = +[];
  @$ary = @$data;
  foreach my $num (0..$data_size-1){
    my $sum = 0;
    for (my $i=0; $i<$data_size; $i++) {
      my $cmp_id = prev($i, $data_size, $num);
      $ary->[$i] = $data->[$cmp_id] if $data->[$cmp_id] < $ary->[$i];
      $sum += $ary->[$i];
    }
    @$data = @$ary;
    $sum += $x*$num;
    $min_sum = $sum if ($min_sum > $sum);
    last if $x*$num > $min_sum;
  }
  return $min_sum;
}

sub prev{
  my ($num, $max, $minus) = @_;
  my $res = $num - $minus;
  $res = $max + $res if $res<0;
  return $res;
}
