The host university is organizing a party for this yearâ€™s
ACM/ICPC contestants with a buffet dinner and $R$ boxes of red wine and $W$ boxes of white wine. Wine boxes
are to be arranged into nonempty piles, each pile contains
only one type of wine, either white or red. After that, those
piles are put into a line so that no two piles belonging to the
same kind sit next to each other. In addition, for security
reasons, each red wine pile should not have more than
$d$ boxes of red wine,
although piles of white wine can be arbitrarily large.
Your task is to identify $K$  the number of different ways to
arrange the given wine boxes satisfying all of the above
conditions.
Input
The input contains $3$
space separated integers in one line: $R$, $W$, $d$ $(1
\leq R,W \leq 10^6, 1 \leq d \leq R)$
Output
Write in one line the remainder of $K$ divided by $10^9+7$.
Sample Clarification
In the first sample below, there are $3$ valid arrangements:
In the second sample below, there are $6$ valid arrangements:
Sample Input 1 
Sample Output 1 
2 2 1

3

Sample Input 2 
Sample Output 2 
2 2 2

6
