Problem2422--Two Bases

2422: Two Bases

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

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Description

time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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 bx and a number Y represented in base by. Compare those two numbers.

Input

The first line of the input contains two space-separated integers n and bx (1≤n≤10, 2≤bx≤40), where n is the number of digits in the bx-based representation of X.

The second line contains n space-separated integers x1,x2,...,xn (0≤xi<bx) − 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 by (1≤m≤10, 2≤by≤40, bx≠by), where m is the number of digits in the by-based representation of Y, and the fourth line contains m space-separated integers y1,y2,...,ym (0≤yi<by) − 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
Examples
Input
6 2
1 0 1 1 1 1
2 10
4 7
Output
=
Input
3 3
1 0 2
2 5
2 4
Output
<
Input
7 16
15 15 4 0 0 7 10
7 9
4 8 0 3 1 5 0
Output
>
Note

In the first sample, X=1011112=4710=Y.

In the second sample, X=1023=215 and Y=245=1123, thus X<Y.

In the third sample, and Y=48031509. We may notice that X starts with much larger digits and bx is much larger than by, so X is clearly larger than Y.

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