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 java.io.IOException;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.HashSet;
import java.util.NoSuchElementException;
import java.util.Objects;
import java.util.PriorityQueue;
import java.util.TreeSet;
import java.util.function.BiFunction;

public class Main{
	static long[][] rpp = new long[1001][1001];
	static long[] rp = new long[1001];
	public static void main(String[] args){
		FastScanner sc = new FastScanner();
		Mathplus mp = new Mathplus();
		PrintWriter out = new PrintWriter(System.out);
		
		int N = sc.nextInt();
		int M = sc.nextInt();
		int d = -1;
		int dn = -1;
		int xor = 0;
		for(int i=0;i<N;i++){
			int f = 0;
			for(int j=0;j<M;j++){
				if(j==0){
					f=sc.nextInt();
					xor ^= f;
				}else{
					int a = sc.nextInt();
					if(a!=f){
						d = i+1;
						dn = j+1;
					}
				}
			}
		}

		if(xor!=0){
			System.out.println("TAK");
			for(int i=0;i<N;i++){
				System.out.print(1+" ");
			}
		}else{
			if(d==-1){
				System.out.println("NIE");
			}else{
				System.out.println("TAK");
				for(int i=0;i<N;i++){
					System.out.print((i+1==d?dn:1)+" ");
				}
			}
		}
	}
}



class SegmentTree<T,E>{
	int N;
	BiFunction<T,T,T> f;
	BiFunction<T,E,T> g;
	T d1;
	ArrayList<T> dat;
	SegmentTree(BiFunction<T,T,T> F,BiFunction<T,E,T> G,T D1,T[] v){
		int n = v.length;
		f = F;
		g = G;
		d1 = D1;
		init(n);
		build(v);
	}
	

	void init(int n) {
		N = 1;
		while(N<n)N*=2;
		dat = new ArrayList<T>();
	}
	
	void build(T[] v) {
		for(int i=0;i<2*N;i++) {
			dat.add(d1);
		}
		for(int i=0;i<v.length;i++) {
			dat.set(N+i-1,v[i]);
		}
		for(int i=N-2;i>=0;i--) {
			dat.set(i,f.apply(dat.get(i*2+1),dat.get(i*2+2)));
		}
	}
	
	void update(int k,E a) {
		k += N-1;
		dat.set(k,g.apply(dat.get(k),a));
		while(k>0){
			k = (k-1)/2;
			dat.set(k,f.apply(dat.get(k*2+1),dat.get(k*2+2)));
		}
	}
	
	T query(int a,int b, int k, int l ,int r) {
		if(r<=a||b<=l) return d1;
		if(a<=l&&r<=b) return dat.get(k);
		T vl = query(a,b,k*2+1,l,(l+r)/2);
		T vr = query(a,b,k*2+2,(l+r)/2,r);
		return f.apply(vl, vr);
	}
	T query(int a,int b){
		return query(a,b,0,0,N);
	}
	
}
	
class LazySegmentTree<T,E> extends SegmentTree<T,E>{
	BiFunction<E,E,E> h;
	BiFunction<E,Integer,E> p = (E a,Integer b) ->{return a;};
	E d0;
	ArrayList<E> laz;
	LazySegmentTree(BiFunction<T,T,T> F,BiFunction<T,E,T> G,BiFunction<E,E,E> H,T D1,E D0,T[] v){
		super(F,G,D1,v);
		int n = v.length;
		h = H;
		d0 = D0;
		Init(n);
	}
	void build() {
		
	}
	void Init(int n){
		laz = new ArrayList<E>();
		for(int i=0;i<2*N;i++) {
			laz.add(d0);
		}
	}
	
	void eval(int len,int k) {
		if(laz.get(k).equals(d0)) return;
		if(k*2+1<N*2-1) {
			laz.set(k*2+1,h.apply(laz.get(k*2+1),laz.get(k)));
			laz.set(k*2+2,h.apply(laz.get(k*2+2),laz.get(k)));
		}
		dat.set(k,g.apply(dat.get(k), p.apply(laz.get(k), len)));
		laz.set(k,d0);
	}
	
	T update(int a,int b,E x,int k,int l,int r) {
		eval(r-l,k);
		if(r<=a||b<=l) {
			return dat.get(k);
		}
		if(a<=l&&r<=b) {
			laz.set(k,h.apply(laz.get(k),x));
			return g.apply(dat.get(k),p.apply(laz.get(k),r-l));
		}
		T vl = update(a,b,x,k*2+1,l,(l+r)/2);
		T vr = update(a,b,x,k*2+2,(l+r)/2,r);
		dat.set(k,f.apply(vl,vr));
		return dat.get(k);
		
	}
	
	T update(int a,int b,E x) {
		return update(a,b,x,0,0,N);
	}
	
	T query(int a,int b,int k,int l,int r) {
		eval(r-l,k);
		if(r<=a||b<=l) return d1;
		if(a<=l&&r<=b) return dat.get(k);
		T vl = query(a,b,k*2+1,l,(l+r)/2);
		T vr = query(a,b,k*2+2,(l+r)/2,r);
		return f.apply(vl, vr);
	}
	
	T query(int a,int b){
		return query(a,b,0,0,N);
	}
	
}
class UnionFindTree {
	int[] root;
	int[] rank;
	int[] size;
	UnionFindTree(int N){
		root = new int[N];
		rank = new int[N];
		size = new int[N];
		for(int i=0;i<N;i++){
			root[i] = i;
			size[i] = 1;
		}
	}

	public int find(int x){
		if(root[x]==x){
			return x;
		}else{
			return find(root[x]);
		}
	}

	public void unite(int x,int y){
		x = find(x);
		y = find(y);
		if(x==y){
			return;
		}else{
			if(rank[x]<rank[y]){
				root[x] = y;
				size[y] += size[x];
			}else{
				root[y] = x;
				size[x] += size[y];
				if(rank[x]==rank[y]){
					rank[x]++;
				}
			}
		}
	}

	public boolean same(int x,int y){
		return find(x)==find(y);
	}
	
}

class ParticalEternalLastingUnionFindTree extends UnionFindTree{
	int[] time;
	int now;
	ParticalEternalLastingUnionFindTree(int N){
		super(N);
		time = new int[N];
		for(int i=0;i<N;i++) {
			time[i] = 1000000007;
		}
	}
	
	public int find(int t,int i) {
		if(time[i]>t) {
			return i;
		}else {
			return find(t,root[i]);
		}
	}
	
	public void unite(int x,int y,int t) {
		now = t;
		x = find(t,x);
		y = find(t,y);
		if(x==y)return;
		if(rank[x]<rank[y]){
			root[x] = y;
			size[y] += size[x];
			time[x] = t;
		}else{
			root[y] = x;
			size[x] += size[y];
			if(rank[x]==rank[y]){
				rank[x]++;
			}
			time[y] = t;
		}
	}
	
	public int sametime(int x,int y) {
		if(find(now,x)!=find(now,y)) return -1;
		int ok = now;
		int ng = 0;
		while(ok-ng>1) {
			int mid = (ok+ng)/2;
			if(find(mid,x)==find(mid,y)) {
				ok = mid;
			}else {
				ng = mid;
			}
		}
		return ok;
	}
	
	
}
class Graph {
	ArrayList<Edge>[] list;
	int size;
	
	TreeSet<LinkEdge> Edges = new TreeSet<LinkEdge>(new LinkEdgeComparator());
	
	@SuppressWarnings("unchecked")
	Graph(int N){
		size = N;
		list = new ArrayList[N];
		for(int i=0;i<N;i++){
			list[i] = new ArrayList<Edge>();
		}
	}
	
	
	void addEdge(int a,int b){
		list[a].add(new Edge(b,1));
	}

	void addWeightedEdge(int a,int b,long c){
		list[a].add(new Edge(b,c));
	}

	void addEgdes(int[] a,int[] b){
		int size = a.length;
		for(int i=0;i<size;i++){
			list[a[i]].add(new Edge(b[i],1));
		}
	}

	void addWeighterEdges(int[] a ,int[] b ,int[] c){
		int size = a.length;
		for(int i=0;i<size;i++){
			list[a[i]].add(new Edge(b[i],c[1]));
		}
	}

	long[] bfs(int s){
		long[] L = new long[size];
		for(int i=0;i<size;i++){
			L[i] = -1;
		}
		L[s] = 0;
		ArrayDeque<Integer> Q = new ArrayDeque<Integer>();
		Q.add(s);

		while(!Q.isEmpty()){
			int v = Q.poll();
			for(Edge e:list[v]){
				int w = e.to;
				long c = e.cost;
				if(L[w]==-1){
					L[w] = L[v] + c;
					Q.add(w);
				}
			}
		}

		return L;
	}
	
	

	long[] dijkstra(int s){
		long[] L = new long[size];
		for(int i=0;i<size;i++){
			L[i] = -1;
		}
		int[] visited = new int[size];
		L[s] = 0;
		PriorityQueue<Pair> Q = new PriorityQueue<Pair>(new SampleComparator());
		Q.add(new Pair(0,s));

		while(!Q.isEmpty()){

			Pair C = Q.poll();
			if(visited[(int)C.b]==0){
				L[(int)C.b] = C.a;
				visited[(int) C.b] = 1;
				for(Edge D:list[(int) C.b]){
					Q.add(new Pair(L[(int)C.b]+D.cost,D.to));
				}
			}
		}

		return L;
	}
	long[] maxtra(int s,long l){
		long[] L = new long[size];
		for(int i=0;i<size;i++){
			L[i] = -1;
		}
		int[] visited = new int[size];
		L[s] = -1;
	;
		PriorityQueue<Pair> Q = new PriorityQueue<Pair>(new SampleComparator());
		Q.add(new Pair(l,s));

		while(!Q.isEmpty()){

			Pair C = Q.poll();
			if(visited[(int)C.b]==0){
				L[(int)C.b] = C.a;
				visited[(int) C.b] = 1;
				for(Edge D:list[(int) C.b]){
					Q.add(new Pair(Math.max(L[(int)C.b],D.cost),D.to));
				}
			}
		}

		return L;
	}
	long Kruskal(){
		long ans = 0;
		for(int i=0;i<size;i++) {
			for(Edge e:list[i]) {
				Edges.add(new LinkEdge(e.cost,i,e.to));
			}
		}
		UnionFindTree UF = new UnionFindTree(size);
		for(LinkEdge e:Edges){
			if(e.a>=0&&e.b>=0) {
				if(!UF.same(e.a,e.b)){
					ans += e.L;
					UF.unite(e.a,e.b);
				}
			}
		}

		return ans;
	}
	
	ArrayList<Integer> Kahntsort(){

		ArrayList<Integer> ans = new ArrayList<Integer>();
		PriorityQueue<Integer> q = new PriorityQueue<Integer>();
		int[] in = new int[size];
		for(int i=0;i<size;i++) {
			for(Edge e:list[i]) {
				in[e.to]++;
			}
		}
		for(int i=0;i<size;i++) {
			if(in[i]==0) {
				q.add(i);
			}
		}
		while(!q.isEmpty()) {
			int v = q.poll();
			ans.add(v);
			for(Edge e:list[v]) {
				in[e.to]--;
				if(in[e.to]==0) {
					q.add(e.to);
				}
			}
		}
		for(int i=0;i<size;i++) {
			if(in[i]>0)return new ArrayList<Integer>();
		}
		return ans;
	}
	
	RootedTree dfsTree(int i) {
		int[] used = new int[size];
		RootedTree r = new RootedTree(size);
		dfsTree(i,used,r);
		return r;
		
	}


	private void dfsTree(int i, int[] used, RootedTree r) {
		used[i] = 1;
		for(Edge e:list[i]) {
			if(used[e.to]==0) {
				r.list[i].add(e);
				used[e.to] = 1;
				dfsTree(i,used,r);
			}
		}
		
	}
}


class Tree extends Graph{
	
	public Tree(int N) {
		super(N);
	}
	
	long[] tyokkei(){
		long[] a = bfs(0);
		
		System.out.println();
		int maxdex = -1;
		long max = 0;
		for(int i=0;i<size;i++){
			if(max<a[i]){
				max = a[i];
				maxdex = i;
			}
		}
 
		long[] b = bfs(maxdex);
		System.out.println();
		int maxdex2 = -1;
		long max2 = 0;
		for(int i=0;i<size;i++){
			if(max2<b[i]){
				max2 = b[i];
				maxdex2 = i;
			}
		}
		long[] ans = {max2,maxdex,maxdex2};
		return ans;
	}
 
}

class RootedTree extends Graph{
	
	RootedTree(int N){
		super(N);
	}
	
}
class LinkEdge{
	long L;
	int a ;
	int b;
	LinkEdge(long l,int A,int B){
		L = l;
		a = A;
		b = B;
	}
	public boolean equals(Object o){
		LinkEdge O = (LinkEdge) o;
		if(O.a==this.a&&O.b==this.b&&O.L==this.L){
			return true;
		}else{
			return false;
		}


	}

	public int hashCode(){
		return Objects.hash(L,a,b);
	}

}

class Edge{
	int to;
	long cost;

	Edge(int a,long b){
		to = a;
		cost = b;
	}

}
class LinkEdgeComparator implements Comparator<LinkEdge>{
	public int compare(LinkEdge P, LinkEdge Q) {
		long temp = P.L-Q.L;
		if(temp==0){
			if(P.a>Q.a){
				return 1;
			}else{
				if(P.b>Q.b){
					return 1;
				}else{
					return -1;
				}
			}

		}
		if(temp>=0){
			return 1;
		}else{
			return -1;
		}
	}

}
class Pair{
	long a;
	long b;

	Pair(long p,long q){
		this.a = p;
		this.b = q;
	}

	public boolean equals(Object o){
		Pair O = (Pair) o;
		if(O.a==this.a&&O.b==this.b){
			return true;
		}else{
			return false;
		}


	}

	public int hashCode(){
		return Objects.hash(a,b);
	}

}

class SampleComparator implements Comparator<Pair>{
	public int compare(Pair P, Pair Q) {
		long temp = P.a-Q.a;
		if(temp==0){
			if(P.b>Q.b){
				return 1;
			}else{
				return -1;
			}

		}
		if(temp>=0){
			return 1;
		}else{
			return -1;
		}
	}

}

class LongIntPair{
	long a;
	int b;

	LongIntPair(long p,int q){
		this.a = p;
		this.b = q;
	}

	public boolean equals(Object o){
		Pair O = (Pair) o;
		if(O.a==this.a&&O.b==this.b){
			return true;
		}else{
			return false;
		}


	}

	public int hashCode(){
		return Objects.hash(a,b);
	}

}

class LongIntSampleComparator implements Comparator<LongIntPair>{
	public int compare(LongIntPair P, LongIntPair Q) {
		long temp = P.a-Q.a;
		if(temp==0){
			if(P.b>Q.b){
				return 1;
			}else{
				return -1;
			}

		}
		if(temp>=0){
			return 1;
		}else{
			return -1;
		}
	}

}

class FastScanner {
    private final java.io.InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    private void skipUnprintable() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;}
    public boolean hasNext() { skipUnprintable(); return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return (minus ? -n : n);
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return (int) (minus ? -n : n);
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
}

class Mathplus{
	int mod = 1000000007;
	long[] fac = new long[1000001];
	long[][] combt = new long[2001][2001];
	long[][] permt = new long[2001][2001];
	boolean isBuild = false;
	boolean isBuildc = false;
	boolean isBuildp = false;
	int mindex = -1;
	int maxdex = -1;


	void buildFac(){
		fac[0] = 1;
		for(int i=1;i<=1000000;i++){
			fac[i] = (fac[i-1] * i)%mod;
		}
		isBuild = true;
	}
	
	void buildComb() {
		for(int i=0;i<=2000;i++) {
			combt[i][0] = 1;
		}
		for(int j=1;j<=2000;j++) {
			combt[j][j] = 1;
			for(int i=j+1;i<=2000;i++) {
				combt[i][j] = combt[i-1][j-1] + combt[i-1][j];
				if(combt[i][j]>=mod)combt[i][j]-=mod;
			}
			
		}
		isBuildc = false;
	}
	
	void buildPerm() {
		for(int i=0;i<=2000;i++) {
			permt[i][0] = 1;
		}
		if(!isBuild)buildFac();
		for(int i=1;i<=2000;i++) {
			for(int j=1;j<=i;j++) {
				permt[i][j] = permt[i][j-1]*(i-j+1);
				permt[i][j] %= mod;
			}
		}
		isBuildp = true;
	}
	
	
	
	public int isBigger(int[] d, int i) {
		int ok = d.length;
		int ng = -1;
		while(Math.abs(ok-ng)>1) {
			int mid = (ok+ng)/2;
			if(d[mid]>i) {
				ok = mid;
			}else {
				ng = mid;
			}
		}
		return ok;
	}
	
	public int isSmaller(int[] d, int i) {
		int ok = -1;
		int ng = d.length;
		while(Math.abs(ok-ng)>1) {
			int mid = (ok+ng)/2;
			if(d[mid]<i) {
				ok = mid;
			}else {
				ng = mid;
			}
		}
		return ok;
	}

	public HashSet<Integer> primetable(int m) {
		HashSet<Integer> pt = new HashSet<Integer>();
		for(int i=2;i<=m;i++) {
			boolean b = true;
			for(int d:pt) {
				if(i%d==0) {
					b = false;
					break;
				}
			}
			if(b) {
				pt.add(i);
			}
		}
		return pt;
	}

	long max(long[] a){
		long max = 0;
		for(int i=0;i<a.length;i++){
			if(max<a[i]){
				max =a[i];
				maxdex = i;
			}
		}
		return max;
	}
	int max(int[] a){
		int max = 0;
		for(int i=0;i<a.length;i++){
			if(max<a[i]){
				max =a[i];
				maxdex = i;
			}
		}
		return max;
	}
	long min(long[] a){
		long min = Long.MAX_VALUE;
		for(int i=0;i<a.length;i++){
			if(min>a[i]){
				min =a[i];
				mindex = i;
			}
		}
		return min;
	}
	int min(int[] a){
		int min = Integer.MAX_VALUE;
		for(int i=0;i<a.length;i++){
			if(min>a[i]){
				min =a[i];
				mindex = i;
			}
		}
		return min;
	}
	long sum(long[] a){
		long sum = 0;
		for(int i=0;i<a.length;i++){
			sum += a[i];
		}
		return sum;
	}
	long sum(int[] a){
		long sum = 0;
		for(int i=0;i<a.length;i++){
			sum += a[i];
		}
		return sum;
	}

	long gcd(long a, long b){
		if(a<b){
			a^=b;
			b^=a;
			a^=b;
		}
		if(a%b==0){
			return b;
		}else{
			return gcd(b,a%b);
		}
	}

	long lcm(long a, long b){
		return a / gcd(a,b) * b;
	}
	
	public long perm(int a,int num) {
		if(a<2000&&num<2000) {
			if(!isBuildp) {
				buildPerm();
				isBuildp = true;
 			}
			return permt[a][num];
		}
		if(!isBuild) {
			buildFac();
		}
		return fac[a] * (rev(fac[a-num]))%mod;
	}
	public long comb(int a,int num){
		if(a<2000&&num<2000) {
			if(!isBuildc) {
				buildComb();
				isBuildc = true;
 			}
			return combt[a][num];
		}
		if(!isBuild){
			buildFac();
		}
		return fac[a] * (rev(fac[num])*rev(fac[a-num])%mod)%mod;
	}

	long rev(long l) {
		return pow(l,mod-2);
	}
	
	long pow(long l, int i) {
		if(i==0){
			return 1;
		}else{
			if(i%2==0){
				long val = pow(l,i/2);
				return val * val % mod;
			}else{
				return pow(l,i-1) * l % mod;
			}
		}
	}


}