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 
#include <bits/stdc++.h>
typedef std::pair<int,int> pii;
int main()
{
    int t;
    std::cin>>t;
    for(int __=0;__!=t;++__){
        int n,m;
        std::cin>>n>>m;
        long long best=0;
        long long espera[n];for(auto&x:espera)std::cin>>x;
        std::string s[n];for(auto&x:s)std::cin>>x;
        std::vector<int> v;
        for(int i=0;i!=(1<<n);++i){
            std::vector<pii> deltas;
            for(int j=0;j!=m;++j){
                long long delta=0;
                for(int k=0;k!=n;++k){
                    if((s[k][j]-'0')==((bool)(i&(1<<k))))++delta;else --delta;
                }
                deltas.push_back({delta,j});
            }
            std::sort(deltas.begin(),deltas.end());
            long long estudantes[n]={};
            long long ans=0;
            for(int j=0;j!=m;++j){
                for(int k=0;k!=n;++k){
                    if(s[k][deltas[j].second]=='1'){
                        estudantes[k]+=j+1;
                    }
                }
            }
           // for(int j=0;j!=n;++j)std::cout<<estudantes[j]<<" ";std::cout<<"\n";
            for(int j=0;j!=n;++j)ans+=abs(estudantes[j]-espera[j]);
            if(best<ans){
                best=ans;
             //   std::cout<<ans<<" a\n";
                v.clear();
                for(int i=0;i!=m;++i)v.push_back(0);
                for(int i=0;i!=m;++i){
                    v[deltas[i].second]=i+1;
                }
            }
        }
       // std::cout<<best<<"\n";
        for(auto&x:v)std::cout<<x<<" ";std::cout<<"\n";
    }
}
