Pillars

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
b₁, …, b_(n), and m white pieces with heights w₁, …, 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 = [a₁, a₂, a₃, a₄]
and B = [b₁, b₂, b₃, b₄] (where a₁ denotes the height of the bottom
(black) piece of the pillar A, a₂ denotes the height of the second
(white) piece of A, and so on), we say that A is more stable than B if
a₁ > b₁, or if a₁ = b₁ but a₂ > b₂, 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 ⋅ 10⁸. The second and third lines
consist respectively of b₁, …, b_(n) and of w₁, …, w_(m). A blank line
separates two cases. Assume 2 ≤ n ≤ 1000 and 2 ≤ m ≤ 1000, and that no
piece has a height larger than 10⁸.

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”.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T12:06:35.733Z

© Jutge.org, 2006–2026.
https://jutge.org
