

IX Olimpiada Informatyczna 2001/2002

Cipher
We are given a sequence of positive integers
a_{i} (for i=1,2,...,n). This
sequence is used to encrypt nbit messages. If we have a
message consisting of consecutive bits
(t_{1},...,t_{n})
(t_{i} is either 0 or 1), then its encryption it the
number:
S=t_{1}a_{1}+t_{2}a_{2}+...+t_{n}a_{n}
Task
You are given encrypted messages and sequences of numbers
(a_{i}), that have been used to encrypt the
messages. Your task is to decrypt the encrypted messages and to save
them in particular files. You are not expected to present any
program. It is sufficient that you write the decrypted messages.
Input
You are given several sets of data at your disposal. Each set is
written in a separate file: szyk.in, where
k is the number of the set. In the first line of each file
there is one integer n, 5<=n<=40. In the
successive n lines there is a sequence of numbers
(a_{i}) written: in the line of number
i+1 there is one positive integer
a_{i}. The sum of the numbers
a_{i} does not exceed
2 000 000 000. In the line of number n+2 there
is one integer S  the encrypted message,
0<=S<=a_{1}+a_{2}+...+a_{n}.
Output
For each set of data szy*.in you should create a file
szy*.out containing the decrypted message. In the first line
of this file you should write the successive numbers
t_{i}, without any spaces between them. The test
data were chosen so that the encrypted messages are unambiguously
determined.
Example
For the following input file szy.in:
24
19226985
123697
67356296
19721773
1113273
69335448
23680077
9029881
85168664
93676782
5253843
77616588
78572630
13375812
17199980
101508862
59248276
3505733
35790095
62028546
85726819
56462819
103373994
91757169
667509506
the correct answer is in the following output file szy.out:
110001000101101100010101
