P5981 [PA 2019] Fibonacci Products

Define the Fibonacci sequence as $F_1=1,F_2=2,F_i=F_{i-1}+F_{i-2}(i\ge 3)$. For any positive integer $x$, we can always write $x$ in a unique Fibonacci representation $(b_1,b_2,...,b_n)$ that satisfies: 1. $b_1\times F_1+b_2\times F_2+...+b_n\times F_n=x$. 2. For any $i(1\le i

The first line contains a positive integer $T$, the number of test cases. Each test case contains two lines, describing the Fibonacci representations of $A$ and $B$. Each line starts with a positive integer $n$, followed by $n$ non-negative integers $b_1,b_2,...,b_n$.

For each test case, output one line. Follow the input format to output the Fibonacci representation of $A\times B$.

For $100\%$ of the testdata, $1\le T\le 10^3$, and the input guarantees that the sum of all $n$ does not exceed $10^6$. Translated by ChatGPT 5