P9699 [GDCPC 2023] X Equals Y

For positive integers $X$ and $b \geq 2$, define $f(X,b)$ as a sequence which describes the base-$b$ representation of $X$, where the $i$-th element in the sequence is the $i$-th least significant digit in the base-$b$ representation of $X$. For example, $f(6, 2) = \{0, 1, 1\}$, while $f(233, 17) = \{12, 13\}$. Given four positive integers $x$, $y$, $A$ and $B$, please find two positive integers $a$ and $b$ satisfying: - $2 \leq a \leq A$ - $2 \leq b \leq B$ - $f(x, a) = f(y, b)$

There are multiple test cases. The first line of the input contains an integer $T$ ($1 \leq T \leq 10^3$) indicating the number of test cases. For each test case: The first line contains four integers $x$, $y$, $A$ and $B$ ($1 \leq x,y \leq 10^9$, $2 \leq A,B \leq 10^9$). It's guaranteed that there are at most $50$ test cases satisfying $\max(x, y) > 10^6$.

For each test case, if valid positive integers $a$ and $b$ do not exist, output $\texttt{NO}$ in one line. Otherwise, first output $\texttt{YES}$ in one line. Then in the next line, output two integers $a$ and $b$ separated by a space. If there are multiple valid answers, you can output any of them.