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
/*
    Problem URL : http://agc004.contest.atcoder.jp/tasks/agc004_b

    Score  :
    Result :
    Time   : ms
    Memory : KB
 */

ini_set('error_reporting', E_ALL & ~E_NOTICE);

fscanf(STDIN, "%d %d", $N, $x);
$a = explode(" ", trim(fgets(STDIN)));
$b = array(array());
$ans = PHP_INT_MAX;

for ($k = 0; $k < $N; $k++) {
    for ($i = 0; $i < $N; $i++) {
        $tmp = $i - $k + $N * ($i < $k);
        if ($k == 0) {
            $b[$k][$i] = $a[$tmp];
        } else {
            $b[$k][$i] = min($b[$k-1][$i], $a[$tmp]);
        }
    }
    $ans = min(array_sum($b[$k]) + $x * $k, $ans);
}

echo $ans . PHP_EOL;
