Codeforces Round 654 (Div. 2) |
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Finished |
A mad scientist Dr.Jubal has made a competitive programming task. Try to solve it!
You are given integers $$$n,k$$$. Construct a grid $$$A$$$ with size $$$n \times n$$$ consisting of integers $$$0$$$ and $$$1$$$. The very important condition should be satisfied: the sum of all elements in the grid is exactly $$$k$$$. In other words, the number of $$$1$$$ in the grid is equal to $$$k$$$.
Let's define:
Find any grid $$$A$$$, which satisfies the following condition. Among such grids find any, for which the value $$$f(A)$$$ is the minimum possible. Among such tables, you can find any.
The input consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases. Next $$$t$$$ lines contain descriptions of test cases.
For each test case the only line contains two integers $$$n$$$, $$$k$$$ $$$(1 \le n \le 300, 0 \le k \le n^2)$$$.
It is guaranteed that the sum of $$$n^2$$$ for all test cases does not exceed $$$10^5$$$.
For each test case, firstly print the minimum possible value of $$$f(A)$$$ among all tables, for which the condition is satisfied.
After that, print $$$n$$$ lines contain $$$n$$$ characters each. The $$$j$$$-th character in the $$$i$$$-th line should be equal to $$$A_{i,j}$$$.
If there are multiple answers you can print any.
4 2 2 3 8 1 0 4 16
0 10 01 2 111 111 101 0 0 0 1111 1111 1111 1111
In the first test case, the sum of all elements in the grid is equal to $$$2$$$, so the condition is satisfied. $$$R_1 = 1, R_2 = 1$$$ and $$$C_1 = 1, C_2 = 1$$$. Then, $$$f(A) = (1-1)^2 + (1-1)^2 = 0$$$, which is the minimum possible value of $$$f(A)$$$.
In the second test case, the sum of all elements in the grid is equal to $$$8$$$, so the condition is satisfied. $$$R_1 = 3, R_2 = 3, R_3 = 2$$$ and $$$C_1 = 3, C_2 = 2, C_3 = 3$$$. Then, $$$f(A) = (3-2)^2 + (3-2)^2 = 2$$$. It can be proven, that it is the minimum possible value of $$$f(A)$$$.
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