P3986 Fibonacci Sequence

Define a sequence: $f(0) = a, f(1) = b, f(n) = f(n - 1) + f(n - 2)$ where $a, b$ are positive integers and $n \geq 2$. How many pairs $(a, b)$ are there such that $k$ appears in this sequence and is not one of the first two terms? Since the answer may be large, you only need to output the result modulo $10^9 + 7$.

One line containing an integer $k$.

One line containing an integer, which is the answer modulo $10^9 + 7$.

$1 \leq k \leq 10^9$. Translated by ChatGPT 5