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 sys
I=lambda:[*map(int,sys.stdin.readline().split())]
prin = sys.stdout.write

t, = I()
for _ in range(t):
	n, m = I()
	expect = I()
	mat = []
	for i in range(n):
		mat.append([*map(int,[*sys.stdin.readline().strip()])])

	big = -1
	perm = None
	for i in range(2 ** n):
		pos = [(i >> j) & 1 for j in range(n)]
		pos = [2 * guy - 1 for guy in pos]
		vals = []
		for j in range(m):
			vals.append(sum(pos[k] * mat[k][j] for k in range(n)))
		order = sorted(zip(vals, range(m)))
		score = []
		qvals = [0] * m
		for j in range(m):
			qvals[order[j][1]] = j + 1
		scores = []
		for k in range(n):
			scores.append(sum(mat[k][j] * qvals[j] for j in range(m)))
		surprise = sum(abs(scores[k] - expect[k]) for k in range(n))
		#print(pos, qvals, surprise)
		if surprise > big:
			big = surprise
			perm = qvals
	prin(' '.join(str(guy for guy in perm)))
	prin('\n')