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문제

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 $a=m⋅q+r$ and $0≤r<m$. 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 $a=m⋅q+r$) 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 $r=3$.

입력

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

출력

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

예제 입력 1

2 5

예제 출력 1

5

예제 입력 2

3 10

예제 출력 2

7

예제 입력 3

3 100

예제 출력 3

7

예제 입력 4

1000000000 1000000007

예제 출력 4

0

예제 입력 5

9 11

예제 출력 5

3

출처

University > University of Alberta Programming Contest > UAPC 2022 B번

  • 문제를 만든 사람: Jiacheng Wu