Petya is a math teacher. n of his students has written a test consisting of m questions. For each student, it is known which questions he has answered correctly and which he has not.

If the student answers the j-th question correctly, he gets p_j points (otherwise, he gets 0 points). Moreover, the points for the questions are distributed in such a way that the array p is a permutation of numbers from 1 to m.

For the i-th student, Petya knows that he expects to get x_i points for the test. Petya wonders how unexpected the results could be. Petya believes that the surprise value of the results for students is equal to ∑_{i=1}^{n} |x_i - r_i|, where r_i is the number of points that the i-th student has got for the test.

Your task is to help Petya find such a permutation p for which the surprise value of the results is maximum possible. If there are multiple answers, print any of them.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.

The first line of each test case contains two integers n and m (1 ≤ n ≤ 10; 1 ≤ m ≤ 10^4) — the number of students and the number of questions, respectively.

The second line contains n integers x_1, x_2, ..., x_n (0 ≤ x_i ≤ (m(m+1))/(2)), where x_i is the number of points that the i-th student expects to get.

This is followed by n lines, the i-th line contains the string s_i (|s_i| = m; s_{i, j} ∈ \{0, 1\}), where s_{i, j} is 1 if the i-th student has answered the j-th question correctly, and 0 otherwise.

The sum of m for all test cases does not exceed 10^4.

Output

For each test case, print m integers — a permutation p for which the surprise value of the results is maximum possible. If there are multiple answers, print any of them.

Example

Input


3
4 3
5 1 2 2
110
100
101
100
4 4
6 2 0 10
1001
0010
0110
0101
3 6
20 3 15
010110
000101
111111


Output


3 1 2 
2 3 4 1 
3 1 4 5 2 6 
import io,os,sys
read = io.BytesIO(os.read(0, os.fstat(0).st_size))
input = lambda: read.readline()
for _ in range(int(input())):
	n,m=map(int,input().split());x=list(map(int,input().split()));l=[]
	for i in range(n):l.append(input().strip())
	c=1<<n;p=[0]*m;ans=-1
	for i in range(c):
		a=[0]*m;b=[0]*n;d=i
		for i in range(n):
			b[i]=d%2;d//=2
		for j in range(n):
			for k in range(m):
				if l[j][k]=='0':continue
				a[k]+=(1 if b[j]==1 else -1)
		s=0;p1=[0]*m
		ar=sorted(list(enumerate(a)),key=lambda x:x[1])
		for i in range(m):p1[ar[i][0]]=i+1
		for i in range(n):
			y=0
			for j in range(m):
				if l[i][j]=='0':continue
				y+=p1[j]
			s+=abs(x[i]-y)
		if s>ans:p=p1[:];ans=s
	print(*p)