class Solution {
public:
long int counter(long long int n) // function to count trailing zeroes in n!
{
long int c=0;
while(n)
{
c+=(n/5);
n/=5;
}
return c;
}
int preimageSizeFZF(int k)
{
// the output is either 5 or 0
// i.e. the count of trailing zeroes changes per 5 numbers
long long int low,high,mid,c;
low=0;
high=1000000000;

    if(k==low || k==high) // t

return 5;

    while(low<=high)
    {
        mid=low+(high-low)/2;
        c = counter(mid);
        if(k==c)   // a number with same no of trailing zeroes is found
            return 5;
        else if(k < c)
            high=mid-1;
        else
            low=mid+1;
    }
    
    return 0;            
}

};

pls upvote if it helps you.