VNOI Marathon 08

Ants

To celebrate the New Year, the ants gather along a circle and play a game together. The queen announces a number, call it M and start by counting 1. In clockwise order, the ants continue to count the next numbers in turn. Who counts M has to go out of the circle. The next ant (in clockwise order) restarts counting from 1.

The game ends when there is only one ant left. This ant will get a new-year gift from the queen.

Given M and the number of ants in the circle, determine the lucky ant that will receive the new-year gift. The ants are numbered in clockwise order, starting from the queen of index 1.

Input

• Line 1: a positive integer N that is the number of ants in the circle.
• Line 2: a postive integer M.

Output

Only one line containing the lucky ant's index.

Constraints

• 1 ≤ N ≤ 10¹².3 ≤ M ≤ 10⁶.
• M ≤ N.

Example

Input
7 
3

Output
4

Output details
The ants 3 6 2 7 5 1 in turn have to go out of the circle.
Ant 4 is the lucky one!