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
import sys
_INPUT_LINES = sys.stdin.read().splitlines()
input = iter(_INPUT_LINES).__next__

def quick_gcd(a,b):
    for i in range(min(a,b),0,-1):
        if a%i==0 and b%i==0:
            return i

def go():
    # n = int(input())
    n, m, a ,b = map(int, input().split())
    # s = sorted(map(int, input().split()))
    # s = input()
    # a,b = min(a,b), max(a,b)
    # s = [input() for _ in range(n)]

    if n*a!=b*m:
        return 'NO'
    row = '1'*a + '0'*(m-a)
    res = []
    g = quick_gcd(m,a)
    pos = 0
    for i in range(n):
        cur = row[pos:]+row[:pos]
        # print (pos, cur)
        res.append(cur)
        pos = (pos + g)%m

    return 'YES' + '\n' + '\n'.join(res)



# x,s = map(int,input().split())
t = int(input())
# t = 1
ans = []
for _ in range(t):
    # print(go())
    ans.append(str(go()))
#
print('\n'.join(ans))
