Problem Statement

For a sequence of integers $P = (P_1, \ldots, P_M)$, let $f(P)$ denote the sequence obtained by inserting $P_i + P_{i+1}$ between $P_i$ and $P_{i+1}$ for each $1\leq i\leq M-1$. More formally:

• Let $Q_i = P_i + P_{i+1}$ for each $1\leq i\leq M - 1$.
• Let $f(P)$ be defined as a sequence of $2M-1$ integers $f(P) = (P_1, Q_1, P_2, Q_2, \ldots, P_{M-1}, Q_{M-1}, P_M)$.

Given are three positive integers $a$, $b$, and $N$ where $a, b\leq N$. Let us begin with a sequence $A = (a, b)$ and define a sequence $B = (B_1, B_2, \ldots)$ as follows.

• Do the following $N$ times: replace $A$ with $f(A)$.
• Then, remove from $A$ all values greater than $N$ and let $B$ be the resulting sequence.

Find $B_L, \ldots, B_R$.

Constraints

• $1\leq N\leq 3\times 10^5$
• $1\leq a, b\leq N$
• $1\leq L\leq R\leq 10^{18}$
• $R - L < 3\times 10^5$
• $R$ is at most the number of elements in the sequence $B$.

Input

Input is given from Standard Input in the following format:

a b N
L R

Output

Print a line containing $B_L, \ldots, B_R$, with a space in between.