3232: Making Sequences is Fun
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Description
time limit per test
2 secondsmemory limit per test
256 megabytesinput
standard inputoutput
standard outputWe'll define S(n) for positive integer n as follows: the number of the n's digits in the decimal base. For example, S(893)=3, S(114514)=6.
You want to make a consecutive integer sequence starting from number m (m,m+1,...). But you need to pay S(n)·k to add the number n to the sequence.
You can spend a cost up to w, and you want to make the sequence as long as possible. Write a program that tells sequence's maximum length.
Input
The first line contains three integers w (1≤w≤1016), m (1≤m≤1016), k (1≤k≤109).
Please, do not write the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.
Output
The first line should contain a single integer − the answer to the problem.
Examples
Input
9 1 1
Output
9
Input
77 7 7
Output
7
Input
114 5 14
Output
6
Input
1 1 2
Output
0