CF1371D.Grid-00100

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:

• $A_{i,j}$ as the integer in the $i$ -th row and the $j$ -th column.
• $R_i = A_{i,1}+A_{i,2}+...+A_{i,n}$ (for all $1 \le i \le n$ ).
• $C_j = A_{1,j}+A_{2,j}+...+A_{n,j}$ (for all $1 \le j \le n$ ).
• In other words, $R_i$ are row sums and $C_j$ are column sums of the grid $A$ .
• For the grid $A$ let's define the value $f(A) = (\max(R)-\min(R))^2 + (\max(C)-\min(C))^2$ (here for an integer sequence $X$ we define $\max(X)$ as the maximum value in $X$ and $\min(X)$ as the minimum value in $X$ ).

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.

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 $f(A)$ .