Task Description
Zeroes
Factorial n is written as n! and n! = 1∗2∗3∗. . .∗(n−1)∗n. For example 2! = 1∗2 = 2, 3! = 1∗2∗3 = 6,
5! = 120, 10! = 3, 628, 800, etc. The function fzero(n) denotes the number of trailing zeroes in n! in
decimal number system. For example fzero(2) = 0, fzero(5) = 1, fzero(10) = 2. Given the domain
of the input parameter v of fzero(v) function, you will have to find out how many different values of
fzero() are there within this range.
Input Format
The input file contains at most 50001 lines of inputs. Each line contains two positive integers low and
high (0 < low ≤ high ≤ 9 ∗ 10^18). Input is terminated by a line containing two zeroes.
Output Format
For each line of input produce one line of output. This line contains an integer D, which denotes how
many different values the function fzero(v) can have if (low ≤ v ≤ high).
Note:
Illustration for Sample input 1: as 1! = 1, 2! = 2, 3! = 6, 4! = 24, 5! = 120, 6! = 720, 7! = 5,040,
8! = 40,320, 9! = 362,880, 10! = 3,628,800, so fzero(1) = 0, fzero(2) = 0, fzero(3) = 0, fzero(4) = 0,
fzero(5) = 1, fzero(6) = 1, fzero(7) = 1, fzero(8) = 1, fzero(9) = 1 and fzero(10) = 2. So in this
range (1 to 10) there are three different values of fzero(v): 0, 1 and 2.
Sample Input
123 1 101 30 0
Sample Output
12 31