Preimage Size of Factorial Zeroes Function

Similar Problems:

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.)

For example, f(3) = 0 because 3! = 6 has no zeroes at the end, while f(11) = 2 because 11! = 39916800 has 2 zeroes at the end. Given K, find how many non-negative integers x have the property that f(x) = K.

Example 1:

Input: K = 0 Output: 5 Explanation: 0!, 1!, 2!, 3!, and 4! end with K = 0 zeroes.

Example 2:

Input: K = 5 Output: 0 Explanation: There is no x such that x! ends in K = 5 zeroes.

Note:

- K will be an integer in the range [0, 10^9].

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