Farmer Bob has two numbers $A$ and $B$, which can be represented as a string of $X$ $9$s and a string of $Y$ $9$s respectively. He wants to find out the product of $A$ and $B$ (which he will call $P$). Bob soon realizes that $P$ will be extremely big, so he will ask $Q$ questions about $P$ instead. For the $i^{\text{th}}$ question, he wants to know the value of the $q_i^{\text{th}}$ digit in $P$ when counting from the left. Can you write a program to help him?

Constraints

For all subtasks:

• $1\le Q\le 5\times {10}^5$
• $q_i$ will not exceed the number of digits in $P$.
• $1\le X,Y\le {10}^{18}$

Points Awarded	Additional Constraints
2 points	$1\le X,Y\le 9$
6 points	$X=1$ and $1\le Y\le {10}^{18}$
7 points	No further constraints

Input Specification

The first line contains three integers $X$, $Y$ and $Q$.

The next $Q$ lines contain an integer $q_i$.

Output Specification

Output $Q$ lines, with the $i^{\text{th}}$ line containing the answer to the $i^{\text{th}}$ question.

Sample Input

3 4 2
1
5

Sample Output

9
0

Explanation for Sample

Since $A=999$ and $B=9999$, $P=999\times 9999=9989001$.