human
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

&lt;

Input

7 16
15 15 4 0 0 7 10
7 9
4 8 0 3 1 5 0

Output

&gt;

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.
Solve the task in PYTHON.
assistant
#Here is Python code to compare those two numbers.

# import sys
# STDIN = sys.stdin
# sys.stdin = open("a.test.txt", "rb");

class Number:
  def __init__(self, length, base):
    self.value = []
    self.base = base
    self.length = length

  def compare(self, other):
    if(self.decimal < other.decimal): return "<"
    if(self.decimal == other.decimal): return "="
    if(self.decimal > other.decimal): return ">"

  @property
  def decimal(self):
    def decimal_generator():
      for i in xrange(self.length):
        j = self.length - (i + 1)
        x = self.value[i]
        yield x * (self.base ** j)
    return sum(decimal_generator())

def main():
  l1, b1 = map(int, raw_input().strip().split())
  v1 = map(int, raw_input().strip().split())
  n1 = Number(l1, b1)
  n1.value = v1

  l2, b2 = map(int, raw_input().strip().split())
  v2 = map(int, raw_input().strip().split())
  n2 = Number(l2, b2)
  n2.value = v2

  print(n1.compare(n2))

if __name__ == "__main__":
    main();