Cayley's Forest
Count the distinct labelled trees on N vertices, modulo 109+7 (a tree is a connected acyclic graph; two trees differ if their edge sets differ).
Input: one integer N.
Output: the number of labelled trees mod 109+7.
Constraints:
- 1 ≤ N ≤ 1018
Sample Tests
Input 1
3
Output 1
3
Input 2
1
Output 2
1
Input 3
2
Output 3
1
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