Long Binary String

2000ms

262144K

Description:

There is a binary string $$$t$$$ of length $$$10^{100}$$$, and initally all of its bits are $$$\texttt{0}$$$. You are given a binary string $$$s$$$, and perform the following operation some times:

Select some substring of $$$t$$$, and replace it with its XOR with $$$s$$$.$$$^\dagger$$$

After several operations, the string $$$t$$$ has exactly two bits $$$\texttt{1}$$$; that is, there are exactly two distinct indices $$$p$$$ and $$$q$$$ such that the $$$p$$$-th and $$$q$$$-th bits of $$$t$$$ are $$$\texttt{1}$$$, and the rest of the bits are $$$\texttt{0}$$$.

Find the lexicographically largest$$$^\ddagger$$$ string $$$t$$$ satisfying these constraints, or report that no such string exists.

$$$^\dagger$$$ Formally, choose an index $$$i$$$ such that $$$0 \leq i \leq 10^{100}-|s|$$$. For all $$$1 \leq j \leq |s|$$$, if $$$s_j = \texttt{1}$$$, then toggle $$$t_{i+j}$$$. That is, if $$$t_{i+j}=\texttt{0}$$$, set $$$t_{i+j}=\texttt{1}$$$. Otherwise if $$$t_{i+j}=\texttt{1}$$$, set $$$t_{i+j}=\texttt{0}$$$.

$$$^\ddagger$$$ A binary string $$$a$$$ is lexicographically larger than a binary string $$$b$$$ of the same length if in the first position where $$$a$$$ and $$$b$$$ differ, the string $$$a$$$ has a bit $$$\texttt{1}$$$ and the corresponding bit in $$$b$$$ is $$$\texttt{0}$$$.

Input:

The only line of each test contains a single binary string $$$s$$$ ($$$1 \leq |s| \leq 35$$$).

Output:

If no string $$$t$$$ exists as described in the statement, output -1. Otherwise, output the integers $$$p$$$ and $$$q$$$ ($$$1 \leq p < q \leq 10^{100}$$$) such that the $$$p$$$-th and $$$q$$$-th bits of the lexicographically maximal $$$t$$$ are $$$\texttt{1}$$$.

Sample Input:

Sample Output:

1 2

Sample Input:

Sample Output:

3 4

Sample Input:

Sample Output:

1 5

Sample Input:

Sample Output:

-1

Sample Input:

00000111110000011111000001111101010

Sample Output:

6 37452687

Note:

In the first test, you can perform the following operations. $$$$$$\texttt{00000}\ldots \to \color{red}{\texttt{1}}\texttt{0000}\ldots \to \texttt{1}\color{red}{\texttt{1}}\texttt{000}\ldots$$$$$$

In the second test, you can perform the following operations. $$$$$$\texttt{00000}\ldots \to \color{red}{\texttt{001}}\texttt{00}\ldots \to \texttt{0}\color{red}{\texttt{011}}\texttt{0}\ldots$$$$$$

In the third test, you can perform the following operations. $$$$$$\texttt{00000}\ldots \to \color{red}{\texttt{1111}}\texttt{0}\ldots \to \texttt{1}\color{red}{\texttt{0001}}\ldots$$$$$$

It can be proven that these strings $$$t$$$ are the lexicographically largest ones.

In the fourth test, you can't make a single bit $$$\texttt{1}$$$, so it is impossible.

Informação

Provedor Codeforces

Código CF1698G