Long route

A robot moves as in the earlier task this week, but now repeats the same command sequence k times. How many distinct squares does the robot visit?

You may assume that the sequence has at most 100 commands, and that k is in the range 1 \dots 10^9

In a file longroute, implement a function count that returns the number of distinct squares visited when given the command sequence and the number of repetitions.

def count(s,k):
    # TODO

if __name__ == "__main__":
    print(count("UR", 100)) # 201
    print(count("UD", 100)) # 2
    print(count("UURRDDL", 500)) # 1506
    print(count("L", 10**9)) # 1000000001
    print(count("DLUR", 10**9)) # 4