Finding the Two Bases

Bessie the cow is taking computing classes at her local college, and she recently learned how to write numbers in different bases.

A number written in base $B$ has digit places representing $1$, $B$, $B^2$, $B^3$, and so on from right to left. In the familiar base $10$ system the places represent $1$, $10$, $100$, $1000$, and so on. The digit sequence $1234$ read in base $10$ means $1(1000) + 2(100) + 3(10) + 4(1)$. The same digit sequence read in base $5$ means $1(125) + 2(25) + 3(5) + 4(1)$, which is $194$ in base $10$. When the base grows, the number represented by a fixed digit sequence grows too. For example, $1234$ in base $7$ is larger than $1234$ in base $6$.

In base $B$ each digit ranges from $0$ to $B-1$, so base $10$ digits run from $0$ to $9$ and base $5$ digits run from $0$ to $4$. Bases larger than $10$ are allowed. Computer scientists often use base $16$, where the letters A to F stand for the digit values $10$ to $15$. In base $16$ the sequence BEEF means $11(4096) + 14(256) + 14(16) + 15$, which is $48879$ in base $10$.

Bases much larger than $10$ interest Bessie. She took a number $N$ and wrote it down in two different bases $X$ and $Y$, both between $10$ and $15000$. In both cases she got a sequence of $3$ digits, and every one of those digits was between $1$ and $9$. Bessie has since forgotten $N$, $X$, and $Y$. Given only the two 3-digit sequences she wrote down, find the two bases $X$ and $Y$ she used.

Because $X$ and $Y$ can be large, a program that tries every possible pair $(X, Y)$ checks nearly $15000^2$ possibilities and does not finish within the time limit.

The first line contains an integer $K$. Each of the next $K$ lines holds one test case, made of two 3-digit numbers. The first is a number $N$ written in base $X$, and the second is the same $N$ written in base $Y$. $N$, $X$, and $Y$ may differ from test case to test case.

Print $K$ lines, one per test case. On each line print $X$ and $Y$ for that test case, separated by a single space. Each test case is guaranteed to have exactly one answer.

The number $8892$ written in base $47$ is $419$, and written in base $35$ it is $792$.