Let's Play with Functions

Bob learned about functions in mathematics class. He considers a function $f$ satisfying the following conditions.

For any real numbers $x,y$,

and

Bob wants to know $f(n)$ for positive integers $n$. Answer his $Q$ queries.

The input is given in the following format:

$Q$ $n_1$ $n_2$

For each query, print $f(n_i)$ modulo $10^9+7$ on its own line, in order.

• $1\le Q\le 1\,000$.
• $1\le n_i\le 10^{200}$ ().