Your task is to count how many numbers in the range [a,b] consist of the digits 2 and 5 only. For example, in the range [1,100] the numbers are 2, 5, 22, 25, 52 and 55, and thus the answer is 6.
In a file twodigit.py, implement the function count_numbers that counts the desired numbers in the range. The function is given the parameters a and b representing the end points of the range.
Your function will be tested using many different ranges. In each test, 1 \le a \le b \le 10^9.
You must implement the function efficiently so that the solution is returned quickly even for long ranges.
def count_numbers(a, b):
# TODO
if __name__ == "__main__":
print(count_numbers(1, 100)) # 6
print(count_numbers(60, 70)) # 0
print(count_numbers(25, 25)) # 1
print(count_numbers(1, 10**9)) # 1022
print(count_numbers(123456789, 987654321)) # 512