Arranging Wine

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 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.

The input contains $3$ space separated integers in one line: $R$, $W$, $d$ $(1 \leq R,W \leq 10^6, 1 \leq d \leq R)$

Write in one line the remainder of $K$ divided by $10^9+7$.

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 |