You are given four positive integers $n$, $m$, $a$, $b$ ($1 \le b \le n \le 50$; $1 \le a \le m \le 50$). Find any such rectangular matrix of size $n \times m$ 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 $t$ ($1 \le t \le 1000$) — the number of test cases. Then $t$ test cases follow.

Each test case is described by four positive integers $n$, $m$, $a$, $b$ ($1 \le b \le n \le 50$; $1 \le a \le m \le 50$), 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 $n \times m$, 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

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import sys\nfrom collections import defaultdict as dd\ndef eprint(*args):\n    print(*args, file=sys.stderr)\nzz=1\nfrom math import *\nimport copy\n#sys.setrecursionlimit(10**6)\nif zz:\n\tinput=sys.stdin.readline\nelse:\t\n\tsys.stdin=open(\'input.txt\', \'r\')\n\tsys.stdout=open(\'all.txt\',\'w\')\ndef li():\n\treturn [int(x) for x in input().split()]\ndef fi():\n\treturn int(input())\ndef si():\n\treturn list(input().rstrip())\t\ndef mi():\n\treturn \tmap(int,input().split())\t\n\ndef bo(i):\n\treturn ord(i)-ord(\'a\')\n\nimport copy\nt=fi()\nwhile t>0:\n\tt-=1\n\tn,m,a,b=mi()\t\n\td=[[\'0\' for i in range(m)] for j in range(n)]\n\ti=0\n\tj=0\n\tflag=0\n\tfor k in range(b*m):\n\t\tif d[i][j]==\'1\':\n\t\t\t#print(i,j,"LOL")\n\t\t\tpp=i-1\n\t\t\twhile i!=pp-1 and d[i][j]==\'1\':\n\t\t\t\ti+=1\n\t\t\t\ti%=n\n\t\t\t\tif d[i][j]==\'0\':\n\t\t\t\t\td[i][j]=\'1\'\n\t\t\t\t\tf=1\n\t\t\t\t\tbreak\n\t\t\ti=(i+1)%n\n\t\t\tj=(j+1)%m\t\t\n\t\t\tif f==0:\n\t\t\t\tflag=1\n\t\t\t\tbreak\n\t\telse:\n\t\t\td[i][j]=\'1\'\n\t\t\ti=(i+1)%n\n\t\t\tj=(j+1)%m\t\n\t\t#print(i,j)\t\t\n\t\t#for ppp in d:\t\t\n\t\t#\tprint(*ppp)\n\n\tif flag:\n\t\tprint("NO")\n\t\tcontinue\t\n\tfor i in range(n):\n\t\tv=0\n\t\tfor j in range(m):\n\t\t\tif d[i][j]==\'1\':\n\t\t\t\tv+=1\n\t\tif v!=a:\n\t\t\tflag=1\n\t\t\tbreak\t\t\n\tif flag:\n\t\tprint("NO")\n\t\tcontinue\n\tprint("YES")\n\tfor i in d\t:\n\t\tprint("".join(i))\t'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 185314