455. Sequence analysis
Time limit per test: 1
second(s)
Memory limit: 4096
kilobytes
input: standard
output: standard
Due to the slow 'mod' and 'div' operations with int64 type, all Delphi solutions for the problem 455 (Sequence analysis) run much slower than the same code written in C++ or Java. We do not guarantee that Delphi solution exists. You are given a sequence of signed 64bit integers defined as follows:
 x_{0} = 1,
 ,
where
mod
is a remainder operator. All arithmetic operations are evaluated without overflow checking. Use standard "remainder" operator for programming languages (it differs from the mathematical version; for example
in programming, while
in mathematics). Use "
long long
" type in C++, "
long
" in Java and "
int64
" in Delphi to store
x_{i} and all other values.
Let's call a sequence element
x_{p} repeatable if it occurs later in the sequence — meaning that there exists such
q,
q >
p, that
x_{q} =
x_{p}. The first repeatable element
M of the sequence is such an element
x_{m} that
x_{m} is repeatable, and none of the
x_{p} where
p <
m are repeatable.
Given
A,
B and
C, your task is to find the index of the second occurence of the first repeatable element
M in the sequence if the index is less or equal to 2 · 10
^{6}. Per definition, the first element of the sequence has index 0.
Input
The only line of input contains three signed 64bit integers:
A,
B and
C (
B > 0,
C > 0).
Output
Print a single integer — the index of the second occurence of the first repeatable member if it is less or equal to 2 · 10
^{6}. Print 1 if the index is more than 2 · 10
^{6}.
Example(s)
sample input

sample output

2 2 9

4

sample input

sample output

2305843009213693951 1 9223372036854775807

5

sample input

sample output

2 1 5

4

Note
In the first sample test the sequence starts with the following numbers: 1, 3, 7, 6, 3, 7. The first repeatable element is 3. The second occurence of 3 has index 4.
In the second sample test the sequence starts with the following numbers: 1, 2305843009213693951, 4611686018427387903, 6917529027641081855, 0, 0, 0. The first repeatable element is 0. The second occurence of 0 has index 5.
In the third sample test the sequence starts with the following numbers: 1, 2, 4, 3, 1, 2, 4. The first repeatable element is 1. The second occurence of 1 has index 4.