Long route

The robot moves as in the earlier exercise this week, but now it repeats the same move sequence $k$ times. How many different squares does the robot visit?

You may assume that the move sequence has at most $100$ moves, and that $k$ is in the range $1 \dots 10^9$. The algorithm should be efficient within these limits.

In a file longroute.py, implement a function count that returns the square count given the move sequence and the repeat count.

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