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

	$data = explode(" ", trim(fgets(STDIN)));
	$n = $data[0];
	$x = $data[1];

    $a = explode(" ", trim(fgets(STDIN)));
    $mina = 10**9 + 7;
    $mini = -1;
    
    for($i=0;$i<$n;$i++){
        if($a[$i] < $mina){
            $mina = $a[$i];
            $mini = $i;
        }
    }
    
    $c = $mini + 1;
    if($c==$n) $c = 0;
    $ans[$mini] = $mina;
    while($c !== $mini){
        $ans[$c] = min($a[$c], $ans[$mini] + $x);
        $c++;
        if($c==$n) $c = 0;
    }
    echo array_sum($ans);
    

?>