Long Binary String
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 $s$.$^\dagger$
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 $\texttt{0}$.
The only line of each test contains a single binary string $s$ ($1 \leq |s| \leq 35$).
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 $\texttt{1}$.
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 $\texttt{1}$.
Samples
1
1 2
001
3 4
1111
1 5
00000
-1
00000111110000011111000001111101010
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.