A Hadamard matrix of order $n$ is an $n \times n$ matrix containing only
$1$s and $1$s, called $H_{n}$, such that $H_{n} \cdot H_{n}^{\top } = n \cdot
I_{n}$ where $I_{n}$ is the $n \times n$ identity matrix. An
interesting property of Hadamard matrices is that they have the
maximum possible determinant of any $n \times n$ matrix with elements in
the range $[1, 1]$.
Hadamard matrices have applications in error correcting codes
and weighing design problems.
The Sylvester construction is a way to create a Hadamard
matrix of size $2n$ given
$H_{n}$. $H_{2n}$ can be constructed
as:
\begin{align*} H_{2n}
& = \left( \begin{array}{ll} H_ n & H_ n \\ H_ n &
H_ n \\ \end{array}\right) \end{align*}
For example:
\begin{align*}
H_{1} & = \left( \begin{array}{l} 1 \\ \end{array}\right)
\\ H_{2} & = \left( \begin{array}{ll} 1 & 1 \\ 1 &
1 \\ \end{array}\right), \end{align*}
and so on. In this problem you are required to print a part
of a Hadamard matrix constructed in the way described
above.
Input
The first number in the input is the number of test cases to
follow. For each test case there are five integers:
$n$, $x$, $y$, $w$ and $h$. $n$ will be between $1$ and $2^{62}$ (inclusive) and will be a
power of $2$. $x$ is the column and $y$ is the row of the upper left
corner of the sub matrix to be printed, and $w$ and $h$ specify the width and height
respectively. Coordinates are zero based, so $0 \le x,y < n$. You can assume
that the sub matrix will fit entirely inside the whole matrix
and that $0 < w,h \le
20$. There will be no more than $1000$ test cases.
Output
For each test case print the sub matrix followed by an empty
line.
Sample Input 1 
Sample Output 1 
3
2 0 0 2 2
4 1 1 3 3
268435456 12345 67890 11 12

1 1
1 1
1 1 1
1 1 1
1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
