Counting Columns

You are standing inside an ancient Measharan monument. It consists of an infinite number of regular hexagonal columns, arranged in a regular hexagonal grid. Each edge of each column is parallel to some line segment between the two nearest columns (like on the picture).

Given the distance between two columns $d$ and the edge length of each column $r$ , compute the number of columns that you can see.

Input

Input consists of several cases. Each case consists of two positive integers: $d$ (distance between the centers of two columns), $r$ (the edge length of each column). You can assume that $2r < d$ , and that $1 \leq d,r \leq 10000$ .

After the last case the input contains a line containing 0 0.

Output

Output the number of visible columns.

We have three consonants and two wovels, say, $a$ , $b$ , $c$ , $d$ , $e$ . According to our definition, there are 5 words of length 1 (all letters), and 25 words of length 2 (all possible pairs of letters). At length 3 the answer is 98 (out of $5^3$ possible words, $3^3$ consists of only wovels, which makes them illegible).

Problem information

Author: Eryk Kopczynski

Generation: 2026-01-25T23:03:57.593Z