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:
import javax.xml.stream.util.EventReaderDelegate;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.security.KeyPair;
import java.util.*;

public class Main {

    static long[][] c ;
    static int[][] arr;
    static int dp[][];
    static int[] parent; /// DSU
    static boolean[][] ans;
    static int n , m;

    public static void main(String[] args) throws IOException {
        Reader.init(System.in);
        n = Reader.nextInt();
        m = Reader.nextInt();
        arr = new int[n][m];
        for (int i = 0 ; i < n ; i++){
            for (int j = 0 ; j  < m ; j++){
                arr[i][j] = Reader.nextInt();
            }
        }
        ans = new boolean[n][m];

        dp = new int[n][1024];

        for (int i = 0 ; i < n ; i++){
            for (int j = 0 ; j < 1024 ; j++){
                dp[i][j] = -1;
            }
        }

        int f = 0;
        for (int i = 0 ; i < m ; i++){
            if (rec(0,i,arr[0][i])==1){
                f = 1;
                break;
            }
            //System.out.println();
        }

        if (f==0){
            System.out.println("NIE");
        }
        else{
            System.out.println("TAK");
            for (int i = 0 ; i < n ; i++){
                for (int j = 0 ; j < m ; j++){
                    if (ans[i][j]){
                        System.out.print((j+1) + " ");
                    }
                }
            }
        }








    }

    static int rec(int row ,int col, int mask){
        //System.out.println(row + " " + col + " " + mask);
        if (row==n-1){
            if (mask!=0){
                ans[row][col] = true;
                return 1;
            }
            return 0;
        }
        if (dp[row][mask]!=-1){
            return dp[row][mask];
        }

        for (int i = 0 ;i < m ; i++){
            if (rec(row+1,i,mask^arr[row+1][i])==1){
                ans[row][col] = true;
                return dp[row][mask] = 1;
            }
        }
        return dp[row][mask]= 0;


    }

    static class Node implements Comparable<Node>{
        int a;
        int b;
        Node(int a , int b){
            this.a  = a;
            this.b  = b;
        }

        @Override
        public int compareTo(Node o) {
            if (this.a != o.a ){
                return this.a - o.a;
            }
            else{
                return this.b - this.b;
            }
        }
    }



    static int find(int a){
        if (parent[a]!=a){
            parent[a] = find(parent[a]);
        }
        return parent[a];
    }




    public static void sortbyColumn_asc(int arr[][], int col)
    {
        // Using built-in sort function Arrays.sort
        Arrays.sort(arr, new Comparator<int[]>() {

            @Override
            // Compare values according to columns
            public int compare(final int[] entry1,
                               final int[] entry2) {

                // To sort in descending order revert
                // the '>' Operator
                if (entry1[col] > entry2[col])
                    return 1;
                else
                    return -1;
            }
        });  // End of function call sort().
    }

    public static void sortbyColumn_dsc(int arr[][], int col)
    {
        // Using built-in sort function Arrays.sort
        Arrays.sort(arr, new Comparator<int[]>() {

            @Override
            // Compare values according to columns
            public int compare(final int[] entry1,
                               final int[] entry2) {

                // To sort in descending order revert
                // the '>' Operator
                if (entry1[col] > entry2[col])
                    return -1;
                else
                    return 1;
            }
        });  // End of function call sort().
    }

    static void swap(char[] arr , int i , int j){
        char tmp = arr[i];
        arr[i] = arr[j];
        arr[j] = tmp;
    }

    static void swap(int[] arr , int i , int j){
        int tmp = arr[i];
        arr[i] = arr[j];
        arr[j] = tmp;
    }





}

class Node implements Comparable<Node>{
    int a ;
    int b;
    Node(int a , int b){
        this.a = a;
        this.b = b;
    }
    public int compareTo(Node o) {
        if (this.a < o.a && this.b < o.b){
            return -1;
        }
        else{
            return 1;
        }
    }
}
class Edge implements Comparable<Edge>{
    int x , y , w;

    public Edge(int x, int y, int w) {
        this.x = x;
        this.y = y;
        this.w = w;
    }

    @Override
    public int compareTo(Edge o) {
        return this.w - o.w;
    }
}
class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
        reader = new BufferedReader(
                new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }
    /** get next word */
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                    reader.readLine() );
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
    static long nextLong() throws IOException {
        return Long.parseLong( next() );
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
}
class MergeSort
{
    // Merges two subarrays of arr[].
    // First subarray is arr[l..m]
    // Second subarray is arr[m+1..r]
    void merge(int arr[], int l, int m, int r)
    {
        // Find sizes of two subarrays to be merged
        int n1 = m - l + 1;
        int n2 = r - m;

        /* Create temp arrays */
        int L[] = new int [n1];
        int R[] = new int [n2];

        /*Copy data to temp arrays*/
        for (int i=0; i<n1; ++i)
            L[i] = arr[l + i];
        for (int j=0; j<n2; ++j)
            R[j] = arr[m + 1+ j];


        /* Merge the temp arrays */

        // Initial indexes of first and second subarrays
        int i = 0, j = 0;

        // Initial index of merged subarry array
        int k = l;
        while (i < n1 && j < n2)
        {
            if (L[i] <= R[j])
            {
                arr[k] = L[i];
                i++;
            }
            else
            {
                arr[k] = R[j];
                j++;
            }
            k++;
        }

        /* Copy remaining elements of L[] if any */
        while (i < n1)
        {
            arr[k] = L[i];
            i++;
            k++;
        }

        /* Copy remaining elements of R[] if any */
        while (j < n2)
        {
            arr[k] = R[j];
            j++;
            k++;
        }
    }

    // Main function that sorts arr[l..r] using
    // merge()
    void sort(int arr[], int l, int r)
    {
        if (l < r)
        {
            // Find the middle point
            int m = (l+r)/2;

            // Sort first and second halves
            sort(arr, l, m);
            sort(arr , m+1, r);

            // Merge the sorted halves
            merge(arr, l, m, r);
        }
    }

    /* A utility function to print array of size n */
    static void printArray(int arr[])
    {
        int n = arr.length;
        for (int i=0; i<n; ++i)
            System.out.print(arr[i] + " ");
        System.out.println();
    }

    // Driver method

}