A 2-3 Recurrence
The sequence obeys f(0)=0, f(1)=1 and f(n)=2f(n−1)+3f(n−2). Print f(N) modulo 109+7.
Input: one integer N.
Output: f(N) mod 109+7.
Constraints:
- 0 ≤ N ≤ 1018
Sample Tests
Input 1
5
Output 1
61
Input 2
0
Output 2
0
Input 3
1
Output 3
1
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