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# Problem F

Chinese Remainder

## 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 $1 \leq n, m \leq 10^9$, $0 \leq a < n$, $0 \leq b < m$. Also, you may assume $\mbox{gcd}(n, m) = 1$.

## Output

For each test case, output two integers $x$, $K$, where $K = nm$ 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 |
---|---|

2 1 2 2 3 151 783 57 278 |
5 6 31471 217674 |