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A. Two Bases

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAfter 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*

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* = 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*.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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