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
def inp():
    return(int(input()))
def inlt():
    return(list(map(int,input().split())))
def insr():
    s = input()
    return(list(s[:len(s) - 1]))
def invr():
    return(map(int,input().split()))
import bisect
#python3 codeforces_1360G.py
def yuh(N,M,A,B):
    times = 1
    for a in range(1,M + 1):
        if (a * N) % M == 0:
            times = a
            break
    original_start = 0
    original_end = A - 1
    for i in range(N):
        start = (i * times + original_start) % M
        end  = (i * times + original_end) % M
        for j in range(M):
            if end < start:
                if j >= start or j <= end:
                        
                    value = 1

                else:
                    value = 0
                if j == M - 1:
                    print(value)
                else:
                    print(value, end = "")
            else:
                if j >= start and j <= end:
                    value = 1

                else:
                    value = 0
                if j == M - 1:
                    print(value)
                else:
                    print(value, end = "")

test_cases = inp()
for test in range(test_cases):
    N,M,A,B = inlt()
    if N * A != M * B:
        print("NO")
        continue
    else:
        print("YES")
        yuh(N,M,A,B)