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:
t=raw_input()
lx=t.split()
k=int(lx[0])
n=int(lx[1])
fav=[]
for i in range(0,k):
    s=raw_input()
    fav.append(s)

for i in range(n):
    s=raw_input()
    fl=0
    if(len(s)<47):
        for j in range(k):
            le=len(fav[j])
            for jjj in range(0,len(s)-le+1):
                if(fav[j]==s[jjj:jjj+le]):
                    fl=1
                    break
    if(fl==1 or len(s)>=47):
        print "Good"
    else:
        print "Bad"