A10117. Two Bases

After seeing the "ALL YOUR BASE ARE BELONG TO US" meme for the first time, numbers $X$ and $Y$ realised that they have different bases, which complicated their relations.

You're given a number $X$ represented in base $b_{x}$ and a number $Y$ represented in base $b_{y}$ . Compare those two numbers.

The first line of the input contains two space-separated integers $n$ and $b_{x}$ ( $1<=n<=10$ , $2<=b_{x}<=40$ ), where $n$ is the number of digits in the $b_{x}$ -based representation of $X$ .

The second line contains $n$ space-separated integers $x_{1},x_{2},...,x_{n}$ ( $0<=x_{i}<b_{x}$ ) — the digits of $X$ . They are given in the order from the most significant digit to the least significant one.

The following two lines describe $Y$ in the same way: the third line contains two space-separated integers $m$ and $b_{y}$ ( $1<=m<=10$ , $2<=b_{y}<=40$ , $b_{x}≠b_{y}$ ), where $m$ is the number of digits in the $b_{y}$ -based representation of $Y$ , and the fourth line contains $m$ space-separated integers $y_{1},y_{2},...,y_{m}$ ( $0<=y_{i}<b_{y}$ ) — the digits of $Y$ .

There will be no leading zeroes. Both $X$ and $Y$ will be positive. All digits of both numbers are given in the standard decimal numeral system.

Output a single character (quotes for clarity):

- '<' if $X<Y$
- '>' if $X>Y$
- '=' if $X=Y$

In the first sample, $X=101111_{2}=47_{10}=Y$ .

In the second sample, $X=102_{3}=21_{5}$ and $Y=24_{5}=112_{3}$ , thus $X<Y$ .

In the third sample,  and $Y=4803150_{9}$ . We may notice that $X$ starts with much larger digits and $b_{x}$ is much larger than $b_{y}$ , so $X$ is clearly larger than $Y$ .