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 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”.