Problem: A Little Elephant from the Zoo of Lviv likes lucky strings, i.e., the strings that consist only of the lucky digits 4 and 7.
The Little Elephant has K favorite lucky strings A1, A2, ..., AK. He thinks that the lucky string S is good if either |S| ≥ 47 or for some j from 1 to K we have that  Aj is a substring of S.
The Little Elephant has found N lucky strings B1, B2, ..., BN under the pillow. Now he wants to know which of them are good. Help him and find for each i from 1 to N whether the string Bi is good or not.
Notes.

Let S be some lucky string. Then


|S| denotes the length of the string S;

S[i] (1 ≤ i ≤ |S|) denotes the i^th character of S (the numeration of characters starts from 1);

The string T of the length M is called a substring of S if for some k from 0 to |S| - M we have 
T[1] = S[k + 1], T[2] = S[k + 2], ..., T[M] = S[k + M].



Input
The first line of the input file contains two integers K and N, the number of favorite lucky strings of the Little Elephant and the number of strings he has found under the pillow. Each of the following K lines contains one favorite lucky string. Namely, j^th line among these K lines contains the string Aj. Each of the following N lines contains one lucky string that was found under the pillow. Namely, i^th line among these N lines contains the string Bi. The input file does not contain any whitespaces.

Output
For each of the N strings that were found under the pillow print Good if it is good, and Bad otherwise.

Constraints
1 ≤ K, N ≤ 50
For each string S in the input file we have 1 ≤ |S| ≤ 50.
Each string in the input file consists only of the lucky digits 4 and 7.


Example


Input:
2 4
47
744
7444
447
7774
77777777777777777777777777777777777777777777774

Output:
Good
Good
Bad
Good



Explanation
The string S = 7444 is good since the favorite string 744 is its substring.
The string S = 447 is good since the favorite string 47 is its substring.
The string S = 7774 is bad since none of the favorite strings 47 and 744 is a substring of S.
The string S = 77777777777777777777777777777777777777777777774 is good since its length is 47. Note, however, that S does not have favorite substrings at all.

Solution (in PYTHON):

Solution:
def luckytest(test,arrl):
	#print "entered"
	#print test
	n=len(test)
	#print "n-m"
	m=len(arrl)
	#print ("%d %d")%(n,m)
	p=False
	i=0;arrt=list(test)
	while(i<m):
		#print "while"
#		print "i"
#		print i
		iter1=len(arrl[i])
		j=0
#		print "iter"
#		print iter1
		while(j+iter1<n+1):
#			print "while-2"
			s=''.join(arrt[j:j+iter1])
#			print "s"
#			print s
			if(s==arrl[i]):
#				print "while-2-if"
				p=True
				return p
			j+=1
		i+=1
	return p

k,n=map(int,raw_input().split())
i=0;arrl=[0]*k
while(i<k):
	arrl[i]=raw_input()
	i+=1
i=0;arrn=[0]*n
#print "arrl"
#print arrl
while(i<n):
	arrn[i]=raw_input()
	i+=1
#print "arrn"
#print arrn
i=0
while(i<n):
	#print "while"
	if(len(arrn[i])>=47):
		print "Good"
	else:
		#print "while-if"
		if( luckytest(arrn[i] , arrl) ):print "Good"
		else: print "Bad"
	i+=1