Preimage Size of Factorial Zeroes Function
Let f(x) be the number of zeroes at the end of x!. Recall that x! = 1 * 2 * 3 * ... * x and, by convention, 0! = 1.
Given an integer k, return the number of non-negative integers x that have the property that f(x) = k.
Example 1
Input
k = 0Output
50!, 1!, 2!, 3!, and 4! end with k = 0 zeroes.
Example 2
Input
k = 5Output
0There is no x such that x! ends in k = 5 zeroes.
Constraints
- 0 <= k <= 10^9