You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
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.

## Input Format
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 $$$10^5$$$.

## Output Format
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.

## Examples
```input
4
2 2
3 8
1 0
4 16
```
```output
0
10
01
2
111
111
101
0
0
0
1111
1111
1111
1111
```

## Note
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 $$$f(A)$$$.

Now solve the problem and return the code.