Buy an Integer

Source: AtCoder

Version: Phuoc Hung OJ Extended

Problem Statement

Integers $1..10^9$ are sold. Integer $N$ costs $AN+B\,d(N)$ where $d(N)$ is its decimal digit count. With budget $X$, find the greatest affordable integer, or 0 if none.

Input

The only line contains $A,B,X$.

Output

Print the greatest affordable integer or 0.

Subtasks

• Subtask 1 — 20%: $A,B,X\le10^6$.
• Subtask 2 — 30%: $X\le10^{12}$.
• Subtask 3 — 50%: $A,B\le10^9$, $X\le10^{18}$.

Example

Input

10 7 100

Output

9

Explanation

9 costs 97, while 10 costs 114.