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 is given from Standard Input in the following format: >$A$ $B$ $X$ #### Constraints - All values in input are integers. - $1 \leq A \leq 10^9$ - $1 \leq B \leq 10^9$ - $1 \leq X \leq 10^{18}$

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

***For Sample #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 ***For Sample #2:*** He can buy the largest integer that is sold. Note that input may not fit into a $32$\-bit integer type.

AtCoder [ABC146C]