Pillars 

The world-famous architect Mr. Fruí from Reus plans 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 on its bottom, a white piece above it, another black piece above, and finally a white piece on the top of the pillar.

Mr. Fruí wishes to know which of the combinations 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), 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 zero ore more test cases. Each test case has on the first line H, an integer between 1 and 4*10⁸. The second and third lines of each test consist respectively of the sequence b₁,..., b_n and of the sequence w₁,..., w_m. A blank line separates two consecutive test cases. You can assume 2$\le$n$\le$100 and 2$\le$m$\le$100, and that no piece has a height larger than 10⁸.

Output 

For every test case, print one line with the sequence of heights of the pieces of the most stable pillar. If no solution exists, print "no solution".

Sample Input 

100
20 20
30 10 30 50
 
100
20 10 4
50 30 45

Sample Output 

20 50 20 10
no solution