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D - Redistribution

Score : $400$ points

Problem Statement

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 $10^9 + 7$.

Constraints

• $1 \leq S \leq 2000$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$S$

Output

Print the answer.

7

3

$3$ sequences satisfy the condition: $\{3,4\}$, $\{4,3\}$ and $\{7\}$.

2

0

There are no sequences that satisfy the condition.

1729

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