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.

Input

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

Output a single character (quotes for clarity):

• '<' if $*X* < *Y*$
• '>' if $*X* > *Y*$
• '=' if $*X* = *Y*$

Note

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 $*Y*$.