2017 Ho Chi Minh City Regional Contest

Start

2017-12-08 02:15 CET

2017 Ho Chi Minh City Regional Contest

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2017-12-08 07:15 CET
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Problem A
Arranging Wine

The host university is organizing a party for this year’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 non-empty 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:

\includegraphics[width=0.7\textwidth ]{1.png}

In the second sample below, there are $6$ valid arrangements:

\includegraphics[width=0.7\textwidth ]{2.png}
Sample Input 1 Sample Output 1
2 2 1
3
Sample Input 2 Sample Output 2
2 2 2
6