Olimpiada Informatyczna

X Olympiad in Informatics 2002/2003

Problem: Sums

Author: Krzysztof Onak

We are given a set of positive integers A. Consider a set of non-negative integers A', such that a number x belongs to A' if and only if x is a sum of some elements from A (the elements may be repeated). For example, if A = {2,5,7}, then sample numbers belonging to the set A' are: 0 (the sum of 0 elements), 2, 4 (2 + 2) and 12 (5 + 7 or 7 + 5 or 2 + 2 + 2 + 2 + 2 + 2); and the following do not belong to A': 1 and 3.

Task

Write a program which:

reads from the standard input the description of the set A and the sequence of numbers b_i,
for each number b_i determines whether it belongs to the set A',
writes the result to the standard output.

Input

In the first line there is one integer n: the number of elements of the set A, 1 <= n <= 5000. The following n lines contain the elements of the set A, one per line. In the (i + 1)-st line there is one positive integer a_i, 1 <= a_i <= 50000. A = {a₁, a₂, ..., a_n}, a₁ < a₂ < ... < a_n.

In the (n + 2)-nd line there is one integer k, 1 <= k <= 10000. Each of the following k lines contains one integer in the range from 0 to 1000000000, they are respectively the numbers b₁, b₂, ..., b_k.

Output

The output should consist of k lines. The i-th line should contain the word TAK ("yes" in Polish), if b_i belongs to A', and it should contain the word NIE ("no") otherwise.

Example

For the following input data:

the correct answer is in the following output:

TAK
NIE
TAK
TAK
NIE
TAK