Today is Krosh's birthday! On this occasion, he baked a huge cake. The cake is a rectangle n × m , divided into nm unit squares by horizontal and vertical cream lines.
Sovunya and Nyusha came to visit Krosh for the holiday. According to the laws of hospitality, Krosh must share his cake with him. To do this, he wants to cut two pieces of the cake in turn and distribute them to the guests.
Krosh can cut a piece of cake like this: divide the cake into two rectangles with one cut passing along one of the horizontal or vertical lines (thus, after the cut, both rectangles have integer side lengths). Next, Krosh chooses one of these rectangles and gives it to the next guest.
After Krosh cuts a piece from his cake twice, he eats the rest himself. Today the cake turned out to be very tasty, and therefore Krosh wants him to get a piece of the largest possible area. Help him determine the maximum area of the cake he can keep.
Input
The first line of the input contains a single integer n ( 1 ≤ n ≤ 4·10
4 ) — cake length. The second line of the input contains a single integer m ( 1 ≤ m ≤ 4·10
4 ) — cake width.
It is guaranteed that two pieces can be cut off from the Krosh cake, leaving a rectangle of non-zero area.
Imprint
Print one number — the maximum area of a piece of cake that Krosh can keep.
Examples
Note
Illustration for the test from the example: Krosh makes cuts along the dotted lines, giving the guests pieces with gray borders. At the end, he gets a piece of size 2 × 3 .
