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 × 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 ≤ i ≤ n). 
  * C_j = A_{1,j}+A_{2,j}+...+A_{n,j} (for all 1 ≤ j ≤ 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

The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 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 ≤ n ≤ 300, 0 ≤ k ≤ 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.

Example

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).

Solution (in PYTHON3):

Solution:
import sys
import heapq
import random
import collections
import bisect

# available on Google, not available on Codeforces
# import numpy as np
# import scipy


def solve(n,k):  # fix inputs here
    cnt = 0
    grid = [[0 for _ in range(n)] for _ in range(n)]
    for i in range(n):
        for j in range(n):
            if cnt == k:
                break
            grid[(j)%n][(i+j)%n] = 1
            cnt += 1

    max_row = 0
    max_col = 0
    min_row = n
    min_col = n
    for row in grid:
        sum_row = sum(row)
        max_row = max(max_row, sum_row)
        min_row = min(min_row, sum_row)

    for row in zip(*grid):
        sum_row = sum(row)
        max_col = max(max_col, sum_row)
        min_col = min(min_col, sum_row)

    print((max_col-min_col)**2 + (max_col - min_col)**2)

    return grid

def console(*args):  # the judge will not read these print statement
    print('\033[36m', *args, '\033[0m', file=sys.stderr)
    return


for case_num in range(int(input())):
    # read line as a string
    # _ = input()

    n,k = list(map(int,input().split()))


    # read line as an integer
    # k = int(input())
    
    # read one line and parse each word as a string
    # lst = input().split()

    # read one line and parse each word as an integer
    # _,_ = list(map(int,input().split()))
    # val = list(map(int,input().split()))
    # ws = list(map(int,input().split()))

    # read matrix and parse as integers (after reading read nrows)
    # lst = list(map(int,input().split()))
    # nrows = lst[0]  # index containing information, please change
    # grid = []
    # for _ in range(nrows):
    #     grid.append(list(map(int,input().split())))

    res = solve(n,k)  # please change
    
    for row in res:
        print("".join([str(x) for x in row]))

    # Google - case number required
    # print("Case #{}: {}".format(case_num+1, res))

    # Codeforces - no case number required
    # print(res)