Pillars P85783

The world-famous architect Mr. Fruí from Reus is planning to build a colossal pillar $H$ units high. Mr. Fruí has $n$ black pieces with heights $b_1, \dots, b_n$, and $m$ white pieces with heights $w_1, \dots, w_m$. According to his design, the pillar must have four pieces: a black piece at its bottom, a white piece above it, another black piece above, and finally a white piece at the top of the pillar.

Mr. Fruí wishes to know which combination of four pieces with total height $H$ is the most stable. Given two combinations $A = [a_1, a_2, a_3, a_4]$ and $B = [b_1, b_2, b_3, b_4]$ (where $a_1$ denotes the height of the bottom (black) piece of the pillar $A$, $a_2$ denotes the height of the second (white) piece of $A$, and so on), we say that $A$ is more stable than $B$ if $a_1 > b_1$, or if $a_1 = b_1$ but $a_2 > b_2$, etc. In other words, $A$ is more stable than $B$ if and only if the sequence of heights of the pieces of $A$ is lexicographically larger than the sequence of heights of the pieces of $B$.

Write a program such that, given the desired height $H$ of the pillar, the heights of the black pieces and the heights of the white pieces, computes which pillar (if any) of height exactly $H$ would be the most stable.

Input

Input consists of several cases, each in three lines. The first line has $H$, an integer number between 1 and $4 \cdot 10^8$. The second and third lines consist respectively of $b_1, \dots, b_n$ and of $w_1, \dots, w_m$. A blank line separates two cases. Assume $2 \le n \le 1000$ and $2 \le m \le 1000$, and that no piece has a height larger than $10^8$.

Output

For every case, print the sequence of heights of the pieces of the most stable pillar, from bottom to top. If no solution exists, print “no solution”.