Description

Input

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

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

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 $f(A)$.