Election the king of monkey in PHP

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Background : 

Amount of monkey N in a circle, identifiering from 1 to N. We choose a random number M to count these monkey, when reaching M, the Mth monkey will be kicked out, and continue, until there is only one luck monkey, he will be the king.

(Is this the algo of Joseph ?  To be verified !)

Program in PHP :

function election($total, $step) {
 $tmp = 0;
 
 for ($i = 2; $i <= $total; $i++) {
     $tmp = ($tmp + $step) % $i;
 }
 
 $winner = $tmp + 1;
 
 return $tmp;
}

If there are other methods to do it more efficient, merci de me dire !