Sequence h=6a+2b (h0=0,h1=1)

Difficulty: 1700 4000 ms 128 MB

math matrix-exponentiation

The sequence has h(0)=0, h(1)=1 and h(n)=6h(n−1)+2h(n−2). Print h(N) modulo 10⁹+7.

Input: one integer N.

Output: h(N) mod 10⁹+7.

Constraints:

• 0 ≤ N ≤ 10¹⁸

Sample Tests

5

1516

0

0

1

1

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