Binary Strings Avoiding 10100

Difficulty: 2100 4000 ms 128 MB

combinatorics kmp matrix-exponentiation

Count the binary strings of length N with no contiguous occurrence of 10100, modulo 10⁹+7.

Input: one integer N.

Output: the count mod 10⁹+7.

Constraints:

• 1 ≤ N ≤ 10¹⁸

Sample Tests

2

4

3

8

5

31

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