## Goal

The rule here is that you start with an element `A1`, and whenever you get to a number you have not seen before, the following term is a **0**. But if the number `An` has appeared previously in the sequence, then you count the number of terms since the last appearance of `An`, and that number is the following term.

For a series starting with `A1` as 0, the series will be:

0, 0, 1, 0, 2, 0, 2, 2, 1, 6, 0, 5, 0, 2, 6, 5, 4, 0, 5, 3, 0, 3, …

Term 1: The first term is 0.

Term 2: Since we haven’t seen 0 before, the second term is 0.

Term 3: Since we had seen a 0 before, one step back, the third term is 1

Term 4: Since we haven’t seen a 1 before, the fourth term is 0

Term 5: Since we had seen a 0 before, two steps back, the fifth term is 2.

And so on...
Input

** Line 1: ** a single integer `A1` that is the first element in the sequence.

** Line 2: ** an integer `N` representing the nth position of an element in the sequence that is to be displayed as output.

Output

A single integer that is the `N`th element of the sequence

Constraints

0 ≤ `A1` ≤ 200

1 ≤ `N` ≤ 1000000