Avoid the Set {aa, bab}

Difficulty: 2400 4000 ms 128 MB

combinatorics aho-corasick matrix-exponentiation

Count the strings of length N over {a, b} that contain none of aa, bab as a substring, modulo 10⁹+7.

Input: one integer N.

Output: the count mod 10⁹+7.

Constraints:

• 1 ≤ N ≤ 10¹⁸

Sample Tests

1

2

2

3

4

4

Read the Editorial