Chinese Remainder Theorem (non-relatively prime moduli)

Input

The first line of input consists of an integers $T$ where $1 \leq T \leq 1000$, the number of test cases. Then follow $T$ lines, each containing four integers $a$, $n$, $b$, $m$ satisfying $1 \leq n, m \leq 10^9$, $0 \leq a < n$, $0 \leq b < m$.

Output

For each test case, output two integers $x$, $K$, where $K = \mbox{lcm}(n,m)$ and $0 \leq x < K$, giving the solution $x \pmod K$ to the equations $x = a \pmod n, x = b \pmod m$.

Sample Input 1 Sample Output 1
3
10000 23000 9000 23000
10000 23000 10000 23000
1234 2000 746 2002
no solution
10000 23000
489234 2002000