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.

### Input

The only line contains integers *n*, *a*, *b*
(1 ≤ *a*, *b* ≤ 300; *max*(*a*,*b*) + 1 ≤ *n* ≤ 50 000).

### Output

Output the number of different record variants modulo 10^{9}+7.

### Sample

### Notes

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