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 = 9\,999~, ~P = 999 \times 9\,999 = 9\,989\,001~.