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
import heapq
import random
import collections

# available on Google, not available on Codeforces
# import numpy as np
# import scipy


from functools import lru_cache



def solve(n,m,a,b):  # fix inputs here
    console(n,m,a,b)
    # if not (n%b == 0 and m%a == 0):
    #     console("case 1a", n%a, m%b, n%b, m%a)
    #     return "NO"

    if n*a != m*b:
        console("case 1b", n/b, m/a)
        return "NO"

    res = []
    t = '1'*a+'0'*(m-a)
    for i in range(n):
        res.append(t)
        t = t[m-a:]+t[:m-a]
    
    return "YES\n" + "\n".join(res)


def console(*args):  # the judge will not read these print statement
    return
    # print('\033[36m', *args, '\033[0m', file=sys.stderr)
    # return


for case_num in range(int(input())):
    # read line as a string
    # strr = input()

    # read line as an integer
    # nrows = int(input())
    
    # read one line and parse each word as a string
    # lst = input().split()

    # read one line and parse each word as an integer
    # _,_ = list(map(int,input().split()))
    n,m,a,b = list(map(int,input().split()))

    # read matrix and parse as integers (after reading read nrows)
    # lst = list(map(int,input().split()))
    # nrows = lst[0]  # index containing information, please change
    # grid = []
    # for _ in range(nrows):
    #     grid.append(input())

    res = solve(n,m,a,b)  # please change
    
    # Google - case number required
    # print("Case #{}: {}".format(case_num+1, res))

    # Codeforces - no case number required
    print(res)
