3423 -- Automaton optimization

Language:

Automaton optimization

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 660		Accepted: 350

Description

Linear cellular automaton is an infinite sequence of cells, each holding either 0 or 1. Cells are indexed with integers, extending from some chosen "zero" cell in both positive and negative directions.

In the initial (first) state all except the finite number of cells contain 0. Next state is computed from previous one by a simple rule: new cell value is 1 if the cell had exactly one neighbour with value 1, otherwise 0.

Although computing states is easy and fast, researchers are often interested in states after very many steps. Because these states may occupy large amount of memory, only parts of them are usually printed.

Your program must, given the initial state, quickly find values for S-th state for cells with indexes F, F + 1, …, F + L − 1.

Input

Input file contains number of non-zero cells in the initial state N, followed by their indexes i₁ i₂... i_N, and then integers S F L. All indexes are different.

Constraints

1 ≤ S ≤ 10⁹, −10⁹ ≤ F ≤ 10⁹, 1 ≤ L, N ≤ 2000, −1000 ≤ i_k ≤ 1000

Output

Output file must contain L values, each of them either 0 or 1.

Sample Input

Sample Input 1
2
1 2
7 -5 5
Sample Input 2
1
0
1 -4 8

Sample Output

Sample Output 1
1 1 0 0 1
Sample Output 2
0 0 0 0 1 0 0 0

Hint

Bold texts appearing in the sample sections are informative and do not form part of the actual data.

Source

Northeastern Europe 2006, Far-Eastern Subregion