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Let be a function acting on strings composed of the digits `0`
and `1`.
The function transforms the string by replacing (independently
and concurrently) every digit `0` with `1` and every digit
`1` with the string .
For example ,
(i.e. assigns an empty string to the empty string).
Note that is an injection, or a one-to-one function.
By we denote the function composed with itself times.
In particular, is the identity function .

We are interested in the strings of the form for This sequence begins with the following strings:

, , , , , .

We call the string a *substring* of the string if it occurs
in as a contiguous (i.e. one-block) subsequence.
A sequence of integers is given.
Your task is to check whether a string of the form
is a substring of for some .

The first line of the standard input contains a single integer , , denoting the number of test units. The first line of each test unit's description contains one integer , . The second line of each description holds non-negative integers , separated by single spaces. The sum of the numbers in the second line of any test unit description does not exceed .

Your programme should print out lines to the standard output,
one for each test unit.
Each line corresponding to a test unit should contain one word:
`TAK` (*yes* in Polish - if
is a substring of
for some in that test unit,
or `NIE` (*no* in Polish) otherwise.

For the input data:

2 2 1 2 2 2 0

the correct result is:

TAK NIE

**Explanation of the example:**
The string from the first test unit is - it is a substring
of for example.
In the second test unit there is a string ,
which is not a substring of for any .

*Task authors: Wojciech Rytter and Bartosz Walczak.*