9644: ABC178 —— D - Redistribution
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Description
Given is an integer $S$. Find how many sequences there are whose terms are all integers greater than or equal to $3$, and whose sum is equal to $S$. The answer can be very large, so output it modulo $10^9 + 7$.
Input
Input is given from Standard Input in the following format:
```
$S$
```
```
$S$
```
Output
Print the answer.
Constraints
- $1 \leq S \leq 2000$
- All values in input are integers.
- All values in input are integers.
Sample 1 Input
7
Sample 1 Output
3
3 sequences satisfy the condition: {3,4}, {4,3} and {7}.
Sample 2 Input
2
Sample 2 Output
0
There are no sequences that satisfy the condition.
Sample 3 Input
1729
Sample 3 Output
294867501