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
# -*- coding:utf-8 -*-

"""

created by shuangquan.huang at 2020/6/4

"""

import collections
import time
import os
import sys
import bisect
import heapq
from typing import List


def gcd(x, y):
    while y:
        x, y = y, x%y
    
    return x


def lcm(a, b):
    c = gcd(a, b)
    return a * b // c


def solve(N, M, A, B):
    if N * A != M * B:
        return False, []
    
    d = lcm(N, M) // N
    matrix = [[0 for _ in range(M)] for _ in range(N)]
    cs = 0
    for r in range(N):
        for c in range(cs, min(cs+A, M)):
            matrix[r][c] = 1
        for c in range(0, A-(M-cs)):
            matrix[r][c] = 1
        cs = (cs + d) % M
    
    return True, matrix
    
    
    


T = int(input())
for ti in range(T):
    N, M, A, B = map(int, input().split())
    a, m = solve(N, M, A, B)
    if not a:
        print('NO')
    else:
        print('YES')
        for row in m:
            print(''.join(map(str, row)))


