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 math_codet;

import java.io.*;
import java.util.*;
 
public class lets_do {
    FastReader in;
    PrintWriter out;
    Helper_class h;
    final long mod = 1000000007;
    final int MAXN = 10000005;
    final int lgN = 20;
    final long INF = (long)1e14;
    final int MAX_Ai = 1000001;
    public static void main(String[] args) throws java.lang.Exception{
        new lets_do().run();
    }
    void run() throws Exception{
        in=new FastReader(System.in);
        out = new PrintWriter(System.out);
        h = new Helper_class();
        int t = 1;
        while(t-->0)
            solve();
        out.flush();
        out.close();
    }
    void solve(){
        int n = h.ni();
        int m = h.ni();
        int[][] arr = new int[n][m];
        TreeSet<Integer> tset = new TreeSet<Integer>();
        int i = 0, j = 0;
        for(i = 0; i < n; i++){
            for(j = 0; j < m; j++){
                arr[i][j] = h.ni();
                //tset.add(arr[i][j]);
            }
        }
        if(tset.size() == 1)
            h.pn("NIE");
        else{
            int xor = 0;
            for(i = 0; i < n; i++)
                xor ^= arr[i][m-1];
            if(xor != 0){
                h.pn("TAK");
                for(i = 0; i < n; i++)
                    h.p(m +" ");
                h.pn("");
            }
            else{
                int ind1 = -1, ind2 = -1;
                boolean found = false;
                for(i = 0; i < n; i++){
                    int curr = xor ^ arr[i][m-1];
                    for(j = 0; j < m; j++){
                        if((curr ^ arr[i][j]) != 0){
                            ind1 = i;
                            ind2 = j;
                            found = true;
                            break;
                        }
                    }
                    if(found)
                        break;
                }
                if(!found)
                    h.pn("NIE");
                else{
                    h.pn("TAK");
                    for(i = 0; i < n; i++){
                        if(i == ind1)
                            h.p(ind2 + 1 +" ");
                        else
                            h.p(m +" ");
                    }
                }
            }
        }
    }   



    static final Comparator<Pair> com = new Comparator<Pair>(){
        public int compare(Pair a, Pair b){
            if(Integer.compare(b.x, a.x) != 0)
                return Integer.compare(b.x, a.x);
            else
                return Long.compare(a.y, b.y);
        }
    };
    
    class Pair{
        int x;
        int y;
        Pair(int p, int q){
            x = p;
            y = q;
        }
    }
    class Edge{
        int u , v;
        Edge(int a, int b){
            u = a;
            v = b;
        }
        int other(int x) {
            return u ^ v ^ x;
        }
    }
    class Helper_class{
        long gcd(long a, long b){return (b==0)?a:gcd(b,a%b);}
        int gcd(int a, int b){return (b==0)?a:gcd(b,a%b);}
        int bitcount(long n){return (n==0)?0:(1+bitcount(n&(n-1)));}
        void p(Object o){out.print(o);}
        void pn(Object o){out.println(o);}
        void pni(Object o){out.println(o);out.flush();}
        String n(){return in.next();}
        String nln(){return in.nextLine();}
        int ni(){return Integer.parseInt(in.next());}
        long nl(){return Long.parseLong(in.next());}
        double nd(){return Double.parseDouble(in.next());}
 
        long mul(long a,long b){
            if(a>=mod)a%=mod;
            if(b>=mod)b%=mod;
            a*=b;
            if(a>=mod)a%=mod;
            return a;
        }
        long modPow(long a, long p){
            long o = 1;
            while(p>0){
                if((p&1)==1)o = mul(o,a);
                a = mul(a,a);
                p>>=1;
            }
            return o;
        }
        long add(long a, long b){
            if(a>=mod)a%=mod;
            if(b>=mod)b%=mod;
            if(b<0)b+=mod;
            a+=b;
            if(a>=mod)a-=mod;
            return a;
        }
    }
 
    class FastReader{
        private InputStream stream; 
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
 
        public FastReader(InputStream stream) {
            this.stream = stream;
        }
 
        public int read() {
            if (numChars == -1)
                throw new UnknownError();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new UnknownError();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
 
        public int peek() {
            if (numChars == -1)
                return -1;
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    return -1;
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar];
        }
 
        public void skip(int x) {
            while (x-- > 0)
                read();
        }
 
        public int nextInt() {
            return Integer.parseInt(next());
        }
 
        public long nextLong() {
            return Long.parseLong(next());
        }
 
        public String nextString() {
            return next();
        }
 
        public String next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuffer res = new StringBuffer();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
 
            return res.toString();
        }
 
        public String nextLine() {
            StringBuffer buf = new StringBuffer();
            int c = read();
            while (c != '\n' && c != -1) {
                if (c != '\r')
                    buf.appendCodePoint(c);
                c = read();
            }
            return buf.toString();
        }
 
        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
 
        public boolean hasNext() {
            int value;
            while (isSpaceChar(value = peek()) && value != -1)
                read();
            return value != -1;
        }
 
        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    }
}