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

__author__ = 'ratmir'

from collections import deque
from math import sqrt

alphabet = "abcdefghijklmnopqrstuvwxyz"


def solve(n, m, a, b):
    if n * a != b * m:
        return False, []
    for d in range(1, m + 1):
        if (d * n) % m == 0:# or a == m:
            rows = []
            matrix = [1] * a + [0] * (m - a)
            rows.append(matrix)

            for i in range(1, n):
                nr = [0] * m
                for j in range(0, m):
                    nr[j] = matrix[(j + m - d) % m]
                rows.append(nr)
                matrix = nr
            return True, rows
    return False, []


def execute():
    [t] = [int(x) for x in sys.stdin.readline().split()]
    results = []
    for ti in range(0, t):
        [n, m, a, b] = [int(x1) for x1 in sys.stdin.readline().split()]

        exists, rows = solve(n, m, a, b)
        if exists:
            s = "YES"
            for row in rows:
                s += "\n"
                s += ''.join('{}'.format(k) for k in row)
            results.append(s)
        else:
            results.append("NO")

    print(''.join('{}\n'.format(k) for k in results))


execute()
