Problem Statement

You are given positive integers $A,B,C,L,R$. Here, $L \leq R$. Define $f(n)=n^3+An^2+Bn+C$. For a non-empty string $S$ consisting of $\mathtt{+}$ and $\mathtt{-}$, define $g(S) = \sum_{i=1}^{|S|} \begin{cases} f(i) & (S_i = \mathtt{+}) \\ -f(i) & (S_i = \mathtt{-}) \end{cases}$. Here, $S_i$ denotes the $i$-th character of $S$. An integer $k$ is said to be generable from $S$ if there exists a non-empty substring $S'$ of $S$ such that $g(S')=k$.

Construct a string $S$ that satisfies the following conditions.

• $1 \leq |S| \leq 2 \times 10^6$
• $S$ is a string consisting of $\mathtt{+}$ and $\mathtt{-}$.
• Among the strings satisfying the two conditions above, $S$ maximizes the number of integers between $L$ and $R$, inclusive, that are generable from $S$.

Furthermore, for the constructed string $S$ and each $k=L,L+1,\dots,R$, determine whether there exist two integers $l,r$ satisfying the following conditions, and if they exist, find one such pair.

• $1 \leq l \leq r \leq |S|$
• Letting $S'$ be the string formed by the $l$-th through $r$-th characters of $S$, we have $g(S')=k$.

What is a substring? A substring of $S$ is a string obtained by deleting zero or more characters from the beginning and zero or more characters from the end of $S$. For example, AB is a substring of ABC, but AC is not a substring of ABC.

Constraints

• $1 \leq A,B,C \leq 10^5$
• $1 \leq L \leq R \leq \min(L+10^5,10^{14})$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

A B C L R

Output

Print a solution in the following format:

S
\mathrm{output}_{L}
\mathrm{output}_{L+1}
\vdots
\mathrm{output}_{R}

Here, $\mathrm{output}_i$ denotes the output for $k=i$. If there exist two integers $l,r$ satisfying the conditions, print them in the following format:

l r

If they do not exist, print -1.

If there are multiple solutions, you may print any of them.