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 gcd

def check(n, m, a, b):
    if m/n == a/b:
        return gcd(m, n)
    return 0

def draw_matrix(n, m, a, b):
    gcd = check(n, m, a, b)
    # print("gcd here `````````````````````", gcd)
    if not gcd:
        return False
    x_kecil, y_kecil = m//gcd, n//gcd
    factor = a//x_kecil
    # print(y_kecil, x_kecil, "========================================")
    matrix = [ [0 for x in range(m)] for y in range(n)]
    for i in range(factor):
        pindah(matrix, i*x_kecil, 0, x_kecil, y_kecil, gcd)
        # print("mulai:", i)
    return matrix
    

def kotak_kecil(matrix, mulai_x, mulai_y, x_kecil, y_kecil):
    for y in range(y_kecil):
        for x in range(x_kecil):
            # print("Assigning", mulai_x + x, mulai_y + y, "to", len(matrix[0]), len(matrix))
            if matrix[mulai_y + y][mulai_x + x] == 1:
                assert False
            matrix[mulai_y + y][mulai_x + x] = 1

def pindah(matrix, mulai_x, mulai_y, x_kecil, y_kecil, gcd):
    for i in range(gcd):
        # print((i*x_kecil + mulai_x) % m, i*y_kecil + mulai_y, x_kecil, y_kecil, "--------------------------------------------")
        kotak_kecil(matrix, (i*x_kecil + mulai_x) % m, i*y_kecil + mulai_y, x_kecil, y_kecil)


if __name__ == "__main__":
    t = int(input())
    for __ in range(t):
        n, m, a, b = map(int, input().split())
        matrix = draw_matrix(n, m, a, b)
        if not matrix:
            print("NO")
            continue
        print("YES")
        for row in matrix:
            print("".join(map(str, row)))

