Putting Plates
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 $$$h$$$ and width $$$w$$$, divided into $$$h \times w$$$ cells. Let $$$(i, j)$$$ denote the cell in the $$$i$$$-th row and the $$$j$$$-th column of the rectangle ($$$1 \le i \le h$$$; $$$1 \le j \le w$$$).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 $$$(i, j)$$$ you put a plate into, at least one of the following conditions must be satisfied: $$$i = 1$$$, $$$i = h$$$, $$$j = 1$$$, $$$j = w$$$.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 $$$(i, j)$$$ contains a plate, you can't put plates into cells $$$(i - 1, j)$$$, $$$(i, j - 1)$$$, $$$(i + 1, j)$$$, $$$(i, j + 1)$$$, $$$(i - 1, j - 1)$$$, $$$(i - 1, j + 1)$$$, $$$(i + 1, j - 1)$$$, $$$(i + 1, j + 1)$$$.Put as many plates on the table as possible without violating the rules above.
For the first test case, example output contains the only way to put $$$6$$$ plates on the table.For the second test case, there are many ways to put $$$4$$$ plates on the table, example output contains one of them.Putting more than $$$6$$$ plates in the first test case or more than $$$4$$$ plates in the second test case is impossible.
The first line contains a single integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases.Each of the following $$$t$$$ lines describes one test case and contains two integers $$$h$$$ and $$$w$$$ ($$$3 \le h, w \le 20$$$) — the height and the width of the table.
For each test case, print $$$h$$$ lines containing $$$w$$$ characters each. Character $$$j$$$ in line $$$i$$$ must be equal to $$$1$$$ if you are putting a plate into cell $$$(i, j)$$$, and $$$0$$$ otherwise. If there are multiple answers, print any.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.
for s in [*open(0)][1:]:
    (h, w) = map(int, s.split())
    print((r := ('10' * w)[:w]), *(['0' * w, '1' + '0' * (w - 2) + '1'] * h)[:h - 3], '0' * w, r)
for _ in range(int(input())):
    (n, k) = map(int, input().split())
    a = [['0'] * k for _ in range(n)]
    for i in range(0, k, 2):
        a[0][i] = '1'
        a[-1][i] = '1'
    if n % 2 == 0:
        for i in range(2, n - 2, 2):
            a[i][0] = '1'
            a[i][-1] = '1'
    else:
        for i in range(2, n - 1, 2):
            a[i][0] = '1'
            a[i][-1] = '1'
    for i in a:
        print(''.join(i))
    print()
from collections import Counter as C
for _ in range(int(input())):
    (n, k) = map(int, input().split())
    a = [['0'] * k for _ in range(n)]
    for i in range(0, k, 2):
        a[0][i] = '1'
        a[-1][i] = '1'
    if n % 2:
        for i in range(2, n - 1, 2):
            a[i][0] = '1'
            a[i][-1] = '1'
    else:
        for i in range(2, n - 2, 2):
            a[i][0] = '1'
            a[i][-1] = '1'
    for x in a:
        print(''.join(x))
    print()