#include <bits/stdc++.h>
const int N = 10;
const int M = 10000;
int n, m, expected[N], ok[N][M], coef[M], cnt[N + N + 1], rank[M];
char buffer[M + 1];
std::pair<int, int> best, order[M];
void dfs(int i, int mask, int coef0) {
  if (i < n) {
    for (int j = 0; j < m; ++j) {
      if (ok[i][j]) {
        coef[j]--;
      }
    }
    dfs(i + 1, mask, coef0 + expected[i]);
    for (int j = 0; j < m; ++j) {
      if (ok[i][j]) {
        coef[j] += 2;
      }
    }
    dfs(i + 1, mask | 1 << i, coef0 - expected[i]);
    for (int j = 0; j < m; ++j) {
      if (ok[i][j]) {
        coef[j]--;
      }
    }
  } else {
    for (int j = 0; j < m; ++j) {
      cnt[n + coef[j]]++;
    }
    int cur = coef0;
    int rank = 1;
    for (int c = -n; c <= n; ++c) {
      while (cnt[n + c] > 0) {
        cur += c * rank;
        rank++;
        cnt[n + c]--;
      }
    }
    best = std::max(best, {cur, mask});
  }
}
int main() {
  int T;
  scanf("%d", &T);
  while (T--) {
    scanf("%d%d", &n, &m);
    for (int i = 0; i < n; ++i) {
      scanf("%d", expected + i);
    }
    for (int i = 0; i < n; ++i) {
      scanf("%s", buffer);
      for (int j = 0; j < m; ++j) {
        ok[i][j] = buffer[j] == '1';
      }
    }
    best = {-1, -1};
    std::fill(coef, coef + m, 0);
    dfs(0, 0, 0);
    int mask = best.second;
    for (int i = 0; i < n; ++i) {
      if (mask >> i & 1) {
        for (int j = 0; j < m; ++j) {
          coef[j] += ok[i][j];
        }
      } else {
        for (int j = 0; j < m; ++j) {
          coef[j] -= ok[i][j];
        }
      }
    }
    for (int j = 0; j < m; ++j) {
      order[j] = {coef[j], j};
    }
    std::sort(order, order + m);
    int cur = 1;
    for (int j = 0; j < m; ++j) {
      rank[order[j].second] = cur++;
    }
    for (int j = 0; j < m; ++j) {
      printf("%d%c", rank[j], " \n"[j + 1 == m]);
    }
  }
}

### Prompt

In Cpp, your task is to solve the following problem:

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>
const int N = 10;
const int M = 10000;
int n, m, expected[N], ok[N][M], coef[M], cnt[N + N + 1], rank[M];
char buffer[M + 1];
std::pair<int, int> best, order[M];
void dfs(int i, int mask, int coef0) {
  if (i < n) {
    for (int j = 0; j < m; ++j) {
      if (ok[i][j]) {
        coef[j]--;
      }
    }
    dfs(i + 1, mask, coef0 + expected[i]);
    for (int j = 0; j < m; ++j) {
      if (ok[i][j]) {
        coef[j] += 2;
      }
    }
    dfs(i + 1, mask | 1 << i, coef0 - expected[i]);
    for (int j = 0; j < m; ++j) {
      if (ok[i][j]) {
        coef[j]--;
      }
    }
  } else {
    for (int j = 0; j < m; ++j) {
      cnt[n + coef[j]]++;
    }
    int cur = coef0;
    int rank = 1;
    for (int c = -n; c <= n; ++c) {
      while (cnt[n + c] > 0) {
        cur += c * rank;
        rank++;
        cnt[n + c]--;
      }
    }
    best = std::max(best, {cur, mask});
  }
}
int main() {
  int T;
  scanf("%d", &T);
  while (T--) {
    scanf("%d%d", &n, &m);
    for (int i = 0; i < n; ++i) {
      scanf("%d", expected + i);
    }
    for (int i = 0; i < n; ++i) {
      scanf("%s", buffer);
      for (int j = 0; j < m; ++j) {
        ok[i][j] = buffer[j] == '1';
      }
    }
    best = {-1, -1};
    std::fill(coef, coef + m, 0);
    dfs(0, 0, 0);
    int mask = best.second;
    for (int i = 0; i < n; ++i) {
      if (mask >> i & 1) {
        for (int j = 0; j < m; ++j) {
          coef[j] += ok[i][j];
        }
      } else {
        for (int j = 0; j < m; ++j) {
          coef[j] -= ok[i][j];
        }
      }
    }
    for (int j = 0; j < m; ++j) {
      order[j] = {coef[j], j};
    }
    std::sort(order, order + m);
    int cur = 1;
    for (int j = 0; j < m; ++j) {
      rank[order[j].second] = cur++;
    }
    for (int j = 0; j < m; ++j) {
      printf("%d%c", rank[j], " \n"[j + 1 == m]);
    }
  }
}

```