## Putting Plates solution codeforces

To celebrate your birthday you have prepared a festive table! Now you want to seat as many guests as possible.

The table can be represented as a rectangle with height hh and width ww, divided into h×wh×w cells. Let (i,j)(i,j) denote the cell in the ii-th row and the jj-th column of the rectangle (1≤i≤h1≤i≤h; 1≤j≤w1≤j≤w).

Into each cell of the table you can either put a plate or keep it empty.

As each guest has to be seated next to their plate, you can only put plates on the edge of the table — into the first or the last row of the rectangle, or into the first or the last column. Formally, for each cell (i,j)(i,j) you put a plate into, at least one of the following conditions must be satisfied: i=1i=1, i=hi=h, j=1j=1, j=wj=w.

To make the guests comfortable, no two plates must be put into cells that have a common side or corner. In other words, if cell (i,j)(i,j) contains a plate, you can’t put plates into cells (i−1,j)(i−1,j), (i,j−1)(i,j−1), (i+1,j)(i+1,j), (i,j+1)(i,j+1), (i−1,j−1)(i−1,j−1), (i−1,j+1)(i−1,j+1), (i+1,j−1)(i+1,j−1), (i+1,j+1)(i+1,j+1).

Put as many plates on the table as possible without violating the rules above.

The first line contains a single integer tt (1≤t≤1001≤t≤100) — the number of test cases.

Each of the following tt lines describes one test case and contains two integers hh and ww (3≤h,w≤203≤h,w≤20) — the height and the width of the table.

For each test case, print hh lines containing ww characters each. Character jj in line ii must be equal to 11 if you are putting a plate into cell (i,j)(i,j), and 00 otherwise.

All plates must be put on the edge of the table. No two plates can be put into cells that have a common side or corner. The number of plates put on the table under these conditions must be as large as possible.

You are allowed to print additional empty lines.

3 3 5 4 4 5 6

10101 00000 10101 0100 0001 1000 0010 010101 000000 100001 000000 101010

For the first test case, example output contains the only way to put 66 plates on the table.

For the second test case, there are many ways to put 44 plates on the table, example output contains one of them.

Putting more than 66 plates in the first test case or more than 44 plates in the second test case is impossible.

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