Allen is tired of playing with alphabet cereal, so he found some binary cereal to play with instead! Allen has $$$n^2$$$ pieces of cereal, each with number $$$0$$$ or $$$1$$$.
This time, Allen is trying to place cereal in an $$$n$$$ x $$$n$$$ grid of cells in order to construct a grid with a Super Rank of 5 or less.
The Super Rank is defined as the number of distinct rows and columns (if the rows were read from left to right, and columns were read from top to bottom).
For example, the binary grid:
| $$$1$$$ | $$$1$$$ | $$$1$$$ |
| $$$1$$$ | $$$0$$$ | $$$0$$$ |
| $$$1$$$ | $$$0$$$ | $$$0$$$ |
Has a super rank of $$$2$$$, since the rows and columns are all $$$111$$$ or $$$100$$$.
Given that Allen has $$$k$$$ pieces of $$$1$$$ cereal and $$$n^2 - k$$$ pieces of $$$0$$$ cereal, output any grid that has a Super Rank of 5 or less.
The first line contains two space seperated integers: $$$n$$$ and $$$k$$$ ($$$1 \leq n \leq 1000$$$, $$$0 \leq k \leq n^2$$$)
Output $$$N$$$ lines, with the $$$i$$$th line being a binary string representing the $$$i$$$th row on the grid.
4 12
1111 0000 1111 1111
This grid has a super rank of 3, which is less than 5: "1111", "1011", "0000".
