Pop-group “Pink elephant” entered on recording their debut album.
In fact they have only two songs: “My love” and “I miss you”,
but each of them has a large number of remixes.
The producer of the group said that the album should consist
of n remixes. On second thoughts the musicians decided
that the album will be of interest only
if there are no more than a remixes on “My love” in a row and
no more than b remixes on “I miss you” in a row.
Otherwise, there is a risk that even the most devoted fans
won’t listen to the disk up to the end.
How many different variants to record the album of interest from n remixes
exist? A variant is a sequence of integers 1 and 2,
where ones denote remixes on “My love” and twos denote remixes on “I miss you”.
Two variants are considered different if for some i in one variant at i-th place stands one
and in another variant at the same place stands two.
The only line contains integers n, a, b
(1 ≤ a, b ≤ 300; max(a,b) + 1 ≤ n ≤ 50 000).
Output the number of different record variants modulo 109+7.
In the example there are the following record variants: 112, 121, 211, 212.
Problem Author: Olga Soboleva (prepared by Alex Samsonov)
Problem Source: NEERC 2014, Eastern subregional contest