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Kosuke is too lazy. He will not give you any legend, just the task:
Fibonacci numbers are defined as follows:
* $f(1)=f(2)=1$. * $f(n)=f(n-1)+f(n-2)$ $(3\le n)$
We denote $G(n,k)$ as an index of the $n$-th Fibonacci number that is divisible by $k$. For given $n$ and $k$, compute $G(n,k)$.
As this number can be too big, output it by modulo $10^9+7$.
For example: $G(3,2)=9$ because the $3$-rd Fibonacci number that is divisible by $2$ is $34$. $[1,1,\textbf{2},3,5,\textbf{8},13,21,\textbf{34}]$.
The first line of the input data contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.
The first and only line contains two integers $n$ and $k$ ($1 \le n \le 10^{18}$, $1 \le k \le 10^5$).
It is guaranteed that the sum of $k$ across all test cases does not exceed $10^6$.
For each test case, output the only number: the value $G(n,k)$ taken by modulo $10^9+7$.
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