#include <bits/stdc++.h>
using namespace std;
const int N = 1e4 + 5;
int T, n, m, x, y;
int ans = 0, All[N], Xi[N], id[N], P[N], who[N];
char s[11][N];
int sgn(int t, int x) {
  if (t == 0)
    return (-1) * x;
  else
    return x;
}
bool cmp(int x, int y) { return Xi[x] < Xi[y]; }
void rmain() {
  cin >> n >> m;
  for (int i = 1; i <= n; ++i) scanf("%d", &All[i]);
  for (int i = 1; i <= n; ++i) scanf("%s", s[i] + 1);
  ans = -1;
  for (int i = 0; i < (1 << n); ++i) {
    for (int j = 1; j <= m; ++j) Xi[j] = 0;
    int res = 0;
    for (int j = 1; j <= n; ++j) {
      res -= sgn(((i >> (j - 1)) & 1), All[j]);
      for (int k = 1; k <= m; ++k) {
        Xi[k] += sgn(((i >> (j - 1)) & 1), s[j][k] - '0');
        id[k] = k;
      }
    }
    sort(id + 1, id + m + 1, cmp);
    for (int j = 1; j <= m; ++j) {
      res += Xi[id[j]] * j;
      who[id[j]] = j;
    }
    if (res >= ans) {
      ans = res;
      for (int j = 1; j <= m; ++j) P[j] = who[j];
    }
  }
  for (int i = 1; i <= m; ++i) printf("%d ", P[i]);
  puts("");
}
int main() {
  for (cin >> T; T--;) rmain();
}

### Prompt

Develop a solution in Cpp to the problem described below:

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 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int N = 1e4 + 5;
int T, n, m, x, y;
int ans = 0, All[N], Xi[N], id[N], P[N], who[N];
char s[11][N];
int sgn(int t, int x) {
  if (t == 0)
    return (-1) * x;
  else
    return x;
}
bool cmp(int x, int y) { return Xi[x] < Xi[y]; }
void rmain() {
  cin >> n >> m;
  for (int i = 1; i <= n; ++i) scanf("%d", &All[i]);
  for (int i = 1; i <= n; ++i) scanf("%s", s[i] + 1);
  ans = -1;
  for (int i = 0; i < (1 << n); ++i) {
    for (int j = 1; j <= m; ++j) Xi[j] = 0;
    int res = 0;
    for (int j = 1; j <= n; ++j) {
      res -= sgn(((i >> (j - 1)) & 1), All[j]);
      for (int k = 1; k <= m; ++k) {
        Xi[k] += sgn(((i >> (j - 1)) & 1), s[j][k] - '0');
        id[k] = k;
      }
    }
    sort(id + 1, id + m + 1, cmp);
    for (int j = 1; j <= m; ++j) {
      res += Xi[id[j]] * j;
      who[id[j]] = j;
    }
    if (res >= ans) {
      ans = res;
      for (int j = 1; j <= m; ++j) P[j] = who[j];
    }
  }
  for (int i = 1; i <= m; ++i) printf("%d ", P[i]);
  puts("");
}
int main() {
  for (cin >> T; T--;) rmain();
}

```