Score : 300 points

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

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

Sample Input 4

1234 56789 314159265