101462: [AtCoder]ABC146 C - Buy an Integer

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 $0$.

Constraints

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

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 $0$.

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