Problem Statement

Takahashi has come to an integer shop to buy an integer.
The shop sells the integers from 1 through 10^9. The integer N is sold for $A \times N + B \times d(N) yen ($the currency of Japan), where d(N) is the number of digits in the decimal notation of N.
Find the largest integer that Takahashi can buy when he has X yen. If no integer can be bought, print 0.

Input

Input is given from Standard Input in the following format:
A B X

Output

Print the greatest integer that Takahashi can buy. If no integer can be bought, print 0.

Constraints

• All values in input are integers.
• $1 \leq A \leq 10^9$
• $1 \leq B \leq 10^9$
• $1 \leq X \leq 10^{18}$

Sample Input 1

10 7 100

Sample Output 1

9

The integer 9 is sold for $10 \times 9 + 7 \times 1 = 97$ yen, and this is the greatest integer that can be bought.
Some of the other integers are sold for the following prices:

• 10: $10 \times 10 + 7 \times 2 = 114$ yen
• 100: $10 \times 100 + 7 \times 3 = 1021$ yen
• 12345: $10 \times 12345 + 7 \times 5 = 123485$ yen

Sample Input 2

2 1 100000000000

Sample Output 2

1000000000

He can buy the largest integer that is sold. Note that input may not fit into a 32-bit integer type.

Sample Input 3

1000000000 1000000000 100

Sample Output 3

0

Sample Input 4

1234 56789 314159265

Sample Output 4

254309

见题面 Input 部分

见题面 Output 部分