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 collections import defaultdict
from itertools import product

t = int(input())
for i in range(t):
    n,m = list(map(int, input().split()))
    store = [defaultdict(int) for i in range(m)]
    strings = []
    for j in range(n):
        s = input()
        strings.append(s)
        for k in range(len(s)):
            store[k][s[k]] += 1
    ans = [set() for i in range(m)]
    for mi in range(len(store)):
        m = store[mi]
        for i,j in m.items():
            ans[mi].add(i)
    test = sorted(ans, key=lambda x: len(x))
    #print(test)
    if len(test) > 1 and len(test[-2]) > 5:
        final = False
    else:
        final = False
        for answer in product(*ans):
            main = answer
            got =True
            for string in strings:
                count = 0
                #print(string, main)
                for ind in range(len(main)):
                    if string[ind]!=main[ind]:
                        count += 1
                    if count > 1:
                        got = False
                        break
                if count > 1:
                    got = False
                    break
            if got:
                print("".join(answer))
                final = True
                break
    if not final:
        print(-1)"""


t = int(input())
for i in range(t):
    n,m,a,b = list(map(int, input().split()))
    #print(n,m,a,b)
    if n*a==m*b:
        print("YES")
        matrix = [["0"]*m for j in range(n)]

        col = 0
        for row in range(n):
            #print("ROW", row, "COLUMN", col)
            tot = 0
            while True:
                if tot==a:
                    break
                #print(row, col,a,b)
                matrix[row][col] = "1"
                col += 1
                tot += 1
                col %= m
            col %= m

        for ma in matrix:
            print("".join(ma))
    else:
        print("NO")