Problem: Student Dima from Kremland has a matrix a of size n × m filled with non-negative integers.

He wants to select exactly one integer from each row of the matrix so that the bitwise exclusive OR of the selected integers is strictly greater than zero. Help him!

Formally, he wants to choose an integers sequence c_1, c_2, …, c_n (1 ≤ c_j ≤ m) so that the inequality a_{1, c_1} ⊕ a_{2, c_2} ⊕ … ⊕ a_{n, c_n} > 0 holds, where a_{i, j} is the matrix element from the i-th row and the j-th column.

Here x ⊕ y denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of integers x and y.

Input

The first line contains two integers n and m (1 ≤ n, m ≤ 500) — the number of rows and the number of columns in the matrix a.

Each of the next n lines contains m integers: the j-th integer in the i-th line is the j-th element of the i-th row of the matrix a, i.e. a_{i, j} (0 ≤ a_{i, j} ≤ 1023). 

Output

If there is no way to choose one integer from each row so that their bitwise exclusive OR is strictly greater than zero, print "NIE".

Otherwise print "TAK" in the first line, in the next line print n integers c_1, c_2, … c_n (1 ≤ c_j ≤ m), so that the inequality a_{1, c_1} ⊕ a_{2, c_2} ⊕ … ⊕ a_{n, c_n} > 0 holds. 

If there is more than one possible answer, you may output any.

Examples

Input


3 2
0 0
0 0
0 0


Output


NIE


Input


2 3
7 7 7
7 7 10


Output


TAK
1 3 

Note

In the first example, all the numbers in the matrix are 0, so it is impossible to select one number in each row of the table so that their bitwise exclusive OR is strictly greater than zero.

In the second example, the selected numbers are 7 (the first number in the first line) and 10 (the third number in the second line), 7 ⊕ 10 = 13, 13 is more than 0, so the answer is found.

Solution (in JAVA):

Solution:
//package com.karancp;
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.io.InputStream;


 public class karan {
    public static void main(String args[])
    {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader z = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        task solver =new task();
        solver.solve(z,out);
        out.close();
    }
    static class task
    {
        static HashMap<String,Boolean> map=new HashMap<>();
        static boolean rec(int ar[][],int mr[][],int i,int p,String s)
        {
            if(i==(ar.length))
            {
                //if(p>0)return false;
                if(p>0)
                {
                    //System.out.println(p);
                    System.out.println("TAK");
                    System.out.println(s);
                    return true;
                }
                else return false;
            }
            else
            {
                String ss=i+" "+p;
                if(map.containsKey(ss))
                {
                   return map.get(ss);
                }
                else {
                    if (rec(ar, mr, i + 1, p ^ (ar[i][mr[i][0] - 1]), s + mr[i][0] + " "))
                    {
                        return true;
                    }
                    else if (rec(ar, mr, i + 1, p ^ ar[i][mr[i][1] - 1], s + mr[i][1] + " "))
                    {
                        return true;
                    }
                    else{
                        map.put(ss,false);
                           return false;
                    }
                }
            }
        }

        public static void solve(InputReader z, PrintWriter out)
        {
           int n=z.nextInt();
           int m=z.nextInt();
           int i;int j;
           int ar[][]=new int[n][m];
           int mr[][]=new int[n][2];
           for(i=0;i<n;i++)
           {
               int max=Integer.MIN_VALUE;
               int min=Integer.MAX_VALUE;
               for(j=0;j<m;j++)
               {
                   ar[i][j]=z.nextInt();
                   if(ar[i][j]>max)
                   {
                       max=ar[i][j];
                       mr[i][1]=j+1;
                   }
                   if(ar[i][j]<min)
                   {
                       min=ar[i][j];
                       mr[i][0]=j+1;
                   }
               }
           }
           if(!rec(ar,mr,0,0,""))
               out.println("NIE");

        }
    }
     static class InputReader {
         public BufferedReader reader;
         public StringTokenizer tokenizer;

         public InputReader(InputStream stream) {
             reader = new BufferedReader(new InputStreamReader(stream), 32768);
             tokenizer = null;
         }

         public String next() {
             while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                 try {
                     tokenizer = new StringTokenizer(reader.readLine());
                 } catch (IOException e) {
                     throw new RuntimeException(e);
                 }
             }
             return tokenizer.nextToken();
         }

         public int nextInt() {
             return Integer.parseInt(next());
         }

     }
}