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
""" Python 3 compatibility tools. """
from __future__ import division, print_function
import itertools
import sys
import os
from io import BytesIO, IOBase


if sys.version_info[0] < 3:
  input = raw_input
  range = xrange

  filter = itertools.ifilter
  map = itertools.imap
  zip = itertools.izip


def is_it_local():
  script_dir = str(os.getcwd()).split('/')
  username = "dipta007"
  return username in script_dir


def READ(fileName):
  if is_it_local():
    sys.stdin = open(f'./{fileName}', 'r')

# region fastio
BUFSIZE = 8192

class FastIO(IOBase):
  newlines = 0

  def __init__(self, file):
    self._fd = file.fileno()
    self.buffer = BytesIO()
    self.writable = "x" in file.mode or "r" not in file.mode
    self.write = self.buffer.write if self.writable else None

  def read(self):
    while True:
      b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
      if not b:
          break
      ptr = self.buffer.tell()
      self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
    self.newlines = 0
    return self.buffer.read()

  def readline(self):
    while self.newlines == 0:
      b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
      self.newlines = b.count(b"\n") + (not b)
      ptr = self.buffer.tell()
      self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
    self.newlines -= 1
    return self.buffer.readline()

  def flush(self):
    if self.writable:
      os.write(self._fd, self.buffer.getvalue())
      self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
  def __init__(self, file):
    self.buffer = FastIO(file)
    self.flush = self.buffer.flush
    self.writable = self.buffer.writable
    self.write = lambda s: self.buffer.write(s.encode("ascii"))
    self.read = lambda: self.buffer.read().decode("ascii")
    self.readline = lambda: self.buffer.readline().decode("ascii")

if not is_it_local():
  sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
  input = lambda: sys.stdin.readline().rstrip("\r\n")

# endregion


def input1(type=int):
  return type(input())


def input2(type=int):
  [a, b] = list(map(type, input().split()))
  return a, b


def input3(type=int):
  [a, b, c] = list(map(type, input().split()))
  return a, b, c


def input_array(type=int):
  return list(map(type, input().split()))


def input_string():
  s = input()
  return list(s)

##############################################################

def check(n, m, res, a, b):
  for i in range(n):
    cnt = 0
    for j in range(m):
      cnt += res[i][j]
    if cnt != a:
      return False
  
  for i in range(m):
    cnt = 0
    for j in range(n):
      cnt += res[j][i]
    
    if cnt != b:
      return False
  
  return True


def main():
  t = input1()
  for ci in range(t):
    [n, m, a, b] = input_array()

    row = [0 for _ in range(n)]
    res = [[0 for _ in range(m)] for _ in range(n)]
    k = 0
    for i in range(n):
      for j in range(a):
        res[i][k%m] = 1
        k += 1
        
    
    # print(res)
    if (check(n, m, res, a, b)):
      print('YES')
      for i in range(n):
        now = "".join(map(str, res[i]))
        print(now)
    else:
      print('NO')
  pass

if __name__ == '__main__':
  READ('in.txt')
  main()
