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
for _ in range(int(input())):
  n, m, a, b = map(int, input().split())
  
  real_result = False
  real_answer = None

  for jump in range(51):
    data = [[0] * m for i in range(n)]
    
    col_count = [0] * m
    row_count = [0] * n
    result = True
    temp = 0
    
    for i in range(n):
      now_row = 0
      for j in range(temp, m + temp):
        if col_count[j % m] == b:
          continue
        else:
          data[i][j % m] = 1
          col_count[j % m] += 1
          row_count[i] += 1
          now_row += 1
          if now_row == a:
            break
      if now_row != a:
        # print("NO")
        # print(data)
        result = False
        break
      temp += jump
    
    if result:
      temp = True
      for i in range(m):
        # print(col_count[i])
        if col_count[i] != b:
          temp = False
      for i in range(n):
        # print(row_count[i])
        if row_count[i] != a:
          temp = False
      if temp:
        real_result = True
        real_answer = data
        break
      else:
        pass

  if real_result:
    print("YES")
    for i in range(n):
      for j in range(m):
        print(data[i][j], end='')
      print()
  else:
    print("NO")