Problem B
Card Divisibility

Since you have learned Modular Arithmetic, you know how to work with quotients and remainders. For every pair of integers $a$ and $m$ with $m>0$, there exist unique integers $q$ and $r$ such that $a = m\cdot q+r$ and $0 \leq r < m$. But this is a bit simple, you wonder if you can do something more interesting with this theory.

Right now, you are holding a handful of consecutive cards numbered from $L$ to $R$. You lay the cards out side-by-side to create a single large number (i.e. concatenating the digits of your cards). You would like to know the remainder (which is the $r$ in $a = m\cdot q + r$) when this number is divided by $9$. For example, $L = 9$ and $R = 11$ means you are holding cards $9, 10, 11$. Concatenating these numbers produces the number $91011$. The remainder $r$ left upon dividing this number by $9$ would be $r = 3$.


Input consists of a single line containing two integers $L$ ($1 \leq L \leq 10^{12}$) and $R$ ($L \leq R \leq 10^{12}$). This means you are holding the cards with numbers from $L$ to $R$, inclusive.


Display a single line containing the remainder of the concatenated number if you were to divide it by $9$.

Sample Input 1 Sample Output 1
2 5
Sample Input 2 Sample Output 2
3 10
Sample Input 3 Sample Output 3
3 100
Sample Input 4 Sample Output 4
1000000000 1000000007
Sample Input 5 Sample Output 5
9 11

Please log in to submit a solution to this problem

Log in