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

-----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, $X = FF 4007 A_{16}$ 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.