Sums

You are given a set $A$ of positive integers. Consider the set $A'$ of non-negative integers where a number $x$ belongs to $A'$ if and only if $x$ can be written as a sum of some elements of $A$ (each element may be used any number of times, including zero times).

For example, if $A = \{2, 5, 7\}$, then $A'$ contains $0$ (the empty sum), $2$, $4$ ($2+2$) and $12$ ($5+7$ or $2+2+2+2+2+2$), while $1$ and $3$ do not belong to $A'$.

Given the description of the set $A$ and a sequence of integers $b_1, b_2, \dots, b_k$, write a program that decides, for each $b_i$, whether it belongs to $A'$.

The first line contains the number of elements $n$ of the set $A$ ($1 \le n \le 5000$). Each of the next $n$ lines contains one element of $A$: the $(i+1)$-th line holds a positive integer $a_i$ ($1 \le a_i \le 50000$), with $a_1 < a_2 < \dots < a_n$, so that $A = \{a_1, a_2, \dots, a_n\}$.

The $(n+2)$-th line contains the number of queries $k$ ($1 \le k \le 10000$). Each of the next $k$ lines contains one integer $b_i$ with $0 \le b_i \le 10^9$.

Print $k$ lines. The $i$-th line must contain TAK (Polish for 'yes') if $b_i$ belongs to $A'$, and NIE (Polish for 'no') otherwise.