Problem C
Colossal Candy Counts
Colin wants to buy some candy. In fact, he wants to buy a colossal amount of candy, but that doesn’t necessarily mean what you think it does. Colin is obsessed with number theory and has invented a type of number called a colossal number.
An integer $n \geq 0$ is called colossal if there exist integers $a,b \geq 0$ such that $a^ b = n$, and the sum of the base-$10$ digits of $n$ is equal to $a$. For example, $512$ is colossal since $8^3 = 512$ and $5 + 1 + 2 = 8$.
Given the minimum and maximum amounts of candy Colin is willing to buy, he needs your help figuring out how many different choices he has if he wants to buy a colossal amount.
Input
The input consists of two space-separated integers, $c_ L$ and $c_ H$, such that $0 \leq c_ L \leq c_ H \leq 10^{12}$.
Output
Output a single line containing the number of colossal integers $c$ in the interval $c_ L \leq c \leq c_ H$.
| Sample Input 1 | Sample Output 1 |
|---|---|
15 5000 |
4 |
| Sample Input 2 | Sample Output 2 |
|---|---|
512 512 |
1 |
