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
from sys import stdin,stdout

def gcd(a,b):
    if(b==0): 
        return a 
    else: 
        return gcd(b,a%b) 

def main():
    t = int(stdin.readline())
    for _ in range (t):
        n,m,a,b = list(map(int, stdin.readline().split()))
        if n * a != m * b:
            stdout.write("NO\n")
            continue
        stdout.write("YES\n")
        arr = []
        g = gcd(max(n,m),min(n,m))
        g = int(m / g)
        pos = 0
        for i in range(n):
            s = ""
            mn = pos
            mx = (pos + m - a) % m
            for j in range(m):
                if mn <= mx:
                    if mn <= j < mx:
                        s += "0"
                    else:
                        s += "1"
                elif mn > mx:
                    if 0 <= j < mx or mn <= j <= m-1:
                        s += "0"
                    else:
                        s += "1"
            pos = (pos + g) % m
            arr.append(s)
        stdout.write("\n".join(arr) + "\n")
        
    
main()