Binary Strings Avoiding 011

Difficulty: 2100 4000 ms 128 MB

combinatorics kmp matrix-exponentiation

Count the binary strings of length N with no contiguous occurrence of 011, modulo 10⁹+7.

Input: one integer N.

Output: the count mod 10⁹+7.

Constraints:

• 1 ≤ N ≤ 10¹⁸

Sample Tests

2

4

3

7

5

20

Read the Editorial