This is an hard version of the problem. The only difference between an easy and a hard version is the constraints on $a$, $b$, $c$ and $d$.

You are given $4$ positive integers $a$, $b$, $c$, $d$ with $a < c$ and $b < d$. Find any pair of numbers $x$ and $y$ that satisfies the following conditions:

• $a < x \leq c$, $b < y \leq d$,
• $x \cdot y$ is divisible by $a \cdot b$.

Note that required $x$ and $y$ may not exist.

The first line of the input contains a single integer $t$ $(1 \leq t \leq 10$), the number of test cases.

The descriptions of the test cases follow.

The only line of each test case contains four integers $a$, $b$, $c$ and $d$ ($1 \leq a < c \leq 10^9$, $1 \leq b < d \leq 10^9$).

For each test case print a pair of numbers $a < x \leq c$ and $b < y \leq d$ such that $x \cdot y$ is divisible by $a \cdot b$. If there are multiple answers, print any of them. If there is no such pair of numbers, then print -1 -1.