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 math import *
t = int(input())
m = []

for i in range(t):
    x = list(map(int, input().split()))
    m.append(x)
for i in range(t):
    flag = 0
    if m[i][0]*m[i][2] == m[i][1]*m[i][3] and m[i][0]>=m[i][3] and m[i][1]>=m[i][2]:
        flag = 1
        print('YES')
        gcd_r= gcd(m[i][0],m[i][3])
        r1 = int(m[i][0]/gcd_r)
        r2 = int(m[i][3]/gcd_r)
        gcd_c = gcd(m[i][1], m[i][2])
        c1 = int(m[i][1] / gcd_c)
        c2 = int(m[i][2] / gcd_c)
        qq = []
        qq += r2 * ['1']
        qq += (r1-r2) * ['0']
        qqq = []
        for kk in range(int(m[i][1]/r1)):
            qqq = qqq + qq

        q4 = []
        str1 = []
        for kk in range(r1):
            qqq.append(qqq.pop(0))
            q4.append(qqq[:])
            str1.append(''.join(q4[kk]))
        for kk in range(m[i][0]):
            print(str1[kk%r1])
    else:
        print('No')