Signal

In a project searching for extraterrestrial intelligence, a signal received from space was recorded as a sequence of integers. The original signal is a sequence $s$ of $n$ integers.

Someone cut this sequence into exactly $k$ consecutive fragments so that no fragment was too short or too long, i.e. every fragment has length between $a$ and $b$ inclusive.

Later a suspicious fragment $f$ of $m$ integers turned up. Decide whether $f$ could really be one of the fragments obtained by cutting the original sequence $s$ as above.

Formally, decide whether $s$ can be split into exactly $k$ consecutive fragments, each of length between $a$ and $b$ inclusive, such that one of those fragments equals $f$ (same length $m$ and the same values in the same order). If it is possible, also report the position in $s$ where that fragment starts (a 1-based index). If several starting positions are possible, report the smallest one.

The first line contains the number of tests $d$ ($1 \le d \le 1000$). The descriptions of the tests follow, one after another.

Each test is given as follows:

• a line with $n$ ($1 \le n \le 10^5$), the length of the original sequence $s$;
• a line with the $n$ integers $s_1, s_2, \dots, s_n$ ($-10^9 \le s_i \le 10^9$) that form the original sequence;
• a line with three integers $a$, $b$, $k$ describing how the sequence is cut ($1 \le a \le b \le n$; $1 \le k \le n$; $a \cdot k \le n \le b \cdot k$);
• a line with $m$ ($a \le m \le b$), the length of the suspicious fragment;
• a line with the $m$ integers $f_1, f_2, \dots, f_m$ ($-10^9 \le f_i \le 10^9$) that form the suspicious fragment $f$.

For each test print a single line. Print NIE if the suspicious fragment $f$ cannot come from the original sequence $s$. Otherwise print TAK followed by a space and the 1-based position in the original sequence where the fragment starts. If several positions are possible, print the smallest one.

The output tokens TAK (yes) and NIE (no) are fixed strings and must be printed exactly as shown.