You are given four positive integers n, m, a, b (1 ≤ b ≤ n ≤ 50; 1 ≤ a ≤ m ≤ 50). Find any such rectangular matrix of size n × m that satisfies all of the following conditions:

  * each row of the matrix contains exactly a ones; 
  * each column of the matrix contains exactly b ones; 
  * all other elements are zeros. 



If the desired matrix does not exist, indicate this.

For example, for n=3, m=6, a=2, b=1, there exists a matrix satisfying the conditions above:

$$$ \begin{vmatrix} 0 & 1 & 0 & 0 & 0 & 1 \\\ 1 & 0 & 0 & 1 & 0 & 0 \\\ 0 & 0 & 1 & 0 & 1 & 0 \end{vmatrix} $$$

Input

The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases. Then t test cases follow.

Each test case is described by four positive integers n, m, a, b (1 ≤ b ≤ n ≤ 50; 1 ≤ a ≤ m ≤ 50), where n and m are the sizes of the matrix, and a and b are the number of ones for rows and columns, respectively.

Output

For each test case print:

  * "YES" (without quotes) and the required matrix (if there are several answers, print any) if it exists, or 
  * "NO" (without quotes) if it does not exist. 



To print the matrix n × m, print n rows, each of which consists of m numbers 0 or 1 describing a row of the matrix. Numbers must be printed without spaces.

Example

Input


5
3 6 2 1
2 2 2 1
2 2 2 2
4 4 2 2
2 1 1 2


Output


YES
010001
100100
001010
NO
YES
11
11
YES
1100
1100
0011
0011
YES
1
1
#
#    ------------------------------------------------
#           ____          _     Generatered using
#          / ___|        | |
#         | |    __ _  __| | ___ _ __  ______ _
#         | |   / _` |/ _` |/ _ \ '_ \|_  / _` |
#         | |__| (_| | (_| |  __/ | | |/ / (_| |
#          \____\____|\____|\___|_| |_/___\____|
#
#      GNU Affero General Public License v3.0
#    ------------------------------------------------
#    Author   : prophet
#    Created  : 2020-07-11 00:28:59.650184
#    UUID     : vM8GYAYv7E21vvSV
#    ------------------------------------------------
#
production = True

import sys, math, collections

def input(input_format = 0, multi = 0):

    if multi > 0: return [input(input_format) for i in range(multi)]
    else:
        next_line = sys.stdin.readline()[:-1]

        if input_format >= 10:
            use_list = False
            input_format = int(str(input_format)[-1])
        else: use_list = True

        if input_format == 0: formatted_input = [next_line]
        elif input_format == 1: formatted_input = list(map(int, next_line.split()))
        elif input_format == 2: formatted_input = list(map(float, next_line.split()))
        elif input_format == 3: formatted_input = list(next_line)
        elif input_format == 4: formatted_input = list(map(int, list(next_line)))
        elif input_format == 5: formatted_input = next_line.split()
        else: formatted_input = [next_line]

        return formatted_input if use_list else formatted_input[0]

def out(output_line, output_format = 0, newline = True):

    formatted_output = ""

    if output_format == 0: formatted_output = str(output_line)
    elif output_format == 1: formatted_output = " ".join(map(str, output_line))
    elif output_format == 2: formatted_output = "\n".join(map(str, output_line))

    print(formatted_output, end = "\n" if newline else "")

def log(*args):
    if not production:
        print("$$$", end = "")
        print(*args)

enu = enumerate

ter = lambda a, b, c: b if a else c

def mapl(iterable, format = 0):
    
    if format == 0: return list(map(int, iterable))
    elif format == 1: return list(map(str, iterable))
    elif format == 2: return list(map(list, iterable))
#
#   >>>>>>>>>>>>>>> START OF SOLUTION <<<<<<<<<<<<<<
#


def solve():

    n, m, a, b = input(1)

    if n * a != m * b:
        out("NO")
        return

    out("YES")

    for i in range(n):
        q = [ter((i * a + j) % m < a, 1, 0) for j in range(m)]
        out("".join(mapl(q, 1)))

    return


for i in range(input(11)): solve()
# solve()

#
#   >>>>>>>>>>>>>>>> END OF SOLUTION <<<<<<<<<<<<<<<
#
