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Problems > Binary Strings Avoiding 101

Binary Strings Avoiding 101

Difficulty: 2100 4000 ms 128 MB

combinatorics kmp matrix-exponentiation

Count the binary strings of length N with no contiguous occurrence of 101, modulo 109+7.

Input: one integer N.

Output: the count mod 109+7.

Constraints:

  • 1 ≤ N ≤ 1018

Sample Tests

Input 1
2
Output 1
4
Input 2
3
Output 2
7
Input 3
5
Output 3
21

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