A. Two Bases
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 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 = 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 b x is much larger than b y, so X is clearly larger than Y.