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
<?php
list($N,$x) = explode(" ",trim(fgets(STDIN)));
$a = explode(" ",trim(fgets(STDIN)));

$min = min($a);
$count = 0;
foreach($a as $key => $val){
    if($val >= $x - $min){
        $count++;
    }else{
        $dp[$key] = $val;
    }
}
if($count == 0){
    echo array_sum($a);
}else{
    $magic = 0;
    while(count($dp) < $N){
        $copy = $dp;
        foreach($copy as $key => $val){
            $num = $key + 1;
            if($key + 1 >= $N){
                $num -= $N;
            }
            $dp[$num] = $val;
        }
        $magic += $x;
        if(count($dp) < $N){
            for($j = 0;$j < $N;$j++){
                if(isset($dp[$j]) == false){
                    if($a[$j] < $magic + $min){
                        $dp[$j] = $a[$j];
                    }
                }
            }
        }
    }
    foreach($dp as $key => $val){
        if($val > $a[$key]){
            $dp[$key] = $a[$key];
        }
    }
    echo array_sum($dp) + $magic;
}