Problem: Ever since Kalevitch, a famous Berland abstractionist, heard of fractals, he made them the main topic of his canvases. Every morning the artist takes a piece of graph paper and starts with making a model of his future canvas. He takes a square as big as n × n squares and paints some of them black. Then he takes a clean square piece of paper and paints the fractal using the following algorithm: 

Step 1. The paper is divided into n2 identical squares and some of them are painted black according to the model.

Step 2. Every square that remains white is divided into n2 smaller squares and some of them are painted black according to the model.

Every following step repeats step 2.

<image>

Unfortunately, this tiresome work demands too much time from the painting genius. Kalevitch has been dreaming of making the process automatic to move to making 3D or even 4D fractals.

Input

The first line contains integers n and k (2 ≤ n ≤ 3, 1 ≤ k ≤ 5), where k is the amount of steps of the algorithm. Each of the following n lines contains n symbols that determine the model. Symbol «.» stands for a white square, whereas «*» stands for a black one. It is guaranteed that the model has at least one white square. 

Output

Output a matrix nk × nk which is what a picture should look like after k steps of the algorithm.

Examples

Input

2 3
.*
..


Output

.*******
..******
.*.*****
....****
.***.***
..**..**
.*.*.*.*
........


Input

3 2
.*.
***
.*.


Output

.*.***.*.
*********
.*.***.*.
*********
*********
*********
.*.***.*.
*********
.*.***.*.

Solution (in JAVA):

Solution:


import java.awt.Point;
import java.io.*;
import java.math.BigInteger;
import java.util.*;
import static java.lang.Math.*;

public class ProblemB_36 {
	
	final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE")!=null;
	BufferedReader in;
	PrintWriter out;
	StringTokenizer tok = new StringTokenizer("");
	
	void init() throws FileNotFoundException{
		in = new BufferedReader(new FileReader("input.txt"));
		out = new PrintWriter("output.txt");
	}
	
	String readString() throws IOException{
		while(!tok.hasMoreTokens()){
			tok = new StringTokenizer(in.readLine());
		}
		return tok.nextToken();
	}
	
	int readInt() throws IOException{
		return Integer.parseInt(readString());
	}
	
	long readLong() throws IOException{
		return Long.parseLong(readString());
	}
	
	double readDouble() throws IOException{
		return Double.parseDouble(readString());
	}
	
	public static void main(String[] args){
		new ProblemB_36().run();
	}
	
	public void run(){
		try{
			long t1 = System.currentTimeMillis();
			init();
			solve();
			out.close();
			long t2 = System.currentTimeMillis();
			System.err.println("Time = "+(t2-t1));
		}catch (Exception e){
			e.printStackTrace(System.err);
			System.exit(-1);
		}
	}
	
	static class Utils {

		private Utils() {}

		public static void mergeSort(int[] a) {
			mergeSort(a, 0, a.length - 1);
		}

		private static void mergeSort(int[] a, int leftIndex, int rightIndex) {
			final int MAGIC_VALUE = 50;
			if (leftIndex < rightIndex) {
				if (rightIndex - leftIndex <= MAGIC_VALUE) {
					insertionSort(a, leftIndex, rightIndex);
				} else {
					int middleIndex = (leftIndex + rightIndex) / 2;
					mergeSort(a, leftIndex, middleIndex);
					mergeSort(a, middleIndex + 1, rightIndex);
					merge(a, leftIndex, middleIndex, rightIndex);
				}
			}
		}

		private static void merge(int[] a, int leftIndex, int middleIndex, int rightIndex) {
			int length1 = middleIndex - leftIndex + 1;
			int length2 = rightIndex - middleIndex;
			int[] leftArray = new int[length1];
			int[] rightArray = new int[length2];
			System.arraycopy(a, leftIndex, leftArray, 0, length1);
			System.arraycopy(a, middleIndex + 1, rightArray, 0, length2);
			for (int k = leftIndex, i = 0, j = 0; k <= rightIndex; k++) {
				if (i == length1) {
					a[k] = rightArray[j++];
				} else if (j == length2) {
					a[k] = leftArray[i++];
				} else {
					a[k] = leftArray[i] <= rightArray[j] ? leftArray[i++] : rightArray[j++];
				}
			}
		}

		private static void insertionSort(int[] a, int leftIndex, int rightIndex) {
			for (int i = leftIndex + 1; i <= rightIndex; i++) {
				int current = a[i];
				int j = i - 1;
				while (j >= leftIndex && a[j] > current) {
					a[j + 1] = a[j];
					j--;
				}
				a[j + 1] = current;
			}
		}

	}
	
	char[][] ex;
	int[] p;
	char[][] c;
	
	void solve() throws IOException{
		int n = readInt();
		int k = readInt();
		ex = new char[n][];
		for (int i = 0; i < n; i++){
			ex[i] = in.readLine().toCharArray();
		}
		p = new int[k+1];
		p[0] = 1;
		for (int i = 1; i <= k; i++){
			p[i] = p[i-1] * n;
		}
		c = new char[p[k]][p[k]];
		build(0, 0, p[k], p[k], k - 1);
		for (int i = 0; i < p[k]; i++){
			for (int j = 0; j < p[k]; j++){
				out.print(c[i][j]);
			}
			out.println();
		}
	}
	
	void build(int ib, int jb, int ie, int je, int k){
		if (k == -1) return;
		for (int i = ib; i < ie; i++){
			for (int j = jb; j < je; j++){
				c[i][j] = ex[(i-ib)/p[k]][(j-jb)/p[k]];
			}
		}
		for (int i = ib; i < ie; i += p[k]){
			for (int j = jb; j < je; j += p[k]){
				if (c[i][j] == '.') build(i, j, i + p[k], j + p[k], k - 1);
			}
		}
	}
	
	static int[][] step8 = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}, {-1, -1}, {1, -1}, {-1, 1}, {1, 1}};
	
	static int[][] stepKnight = {{-2, -1}, {-2, 1}, {-1, -2}, {-1, 2}, {1, -2}, {1, 2}, {2, -1}, {2, 1}};
	
	static long gcd(long a, long b){
		if (a == 0)	return b;
		return gcd(b % a, a);
	}
	
	static long lcm(long a, long b){
		return a / gcd(a, b)*b;
	}

	static long[] gcdPlus(long a, long b){
		long[] d = new long[3];
		if (a == 0){
			d[0] = b;
			d[1] = 0;
			d[2] = 1;
		}else{
			d = gcdPlus(b % a, a);
			long r = d[1];
			d[1] = d[2] - b/a*d[1];
			d[2] = r;
		}
		return d;
	}
	
	static long binpow(long a, int n){
		if (n == 0)	return 1;
		if ((n & 1) == 0){
			long b = binpow(a, n/2);
			return b*b;
		}else return binpow(a, n - 1)*a;
	}
	
	static long binpowmod(long a, int n, long m){
		if (m == 1) return 0;
		if (n == 0)	return 1;
		if ((n & 1) == 0){
			long b = binpowmod(a, n/2, m);
			return (b*b) % m;
		}else return binpowmod(a, n - 1, m)*a % m;
	}
	
	static long phi(long n){
		int[] p = Sieve((int)ceil(sqrt(n)) + 2);
		long phi = 1;
		for (int i = 0; i < p.length; i++){
			long x = 1;
			while (n % p[i] == 0){
				n /= p[i];
				x *= p[i];
			}
			phi *= x - x/p[i];
		}
		if (n != 1) phi *= n - 1;
		return phi;
	}
	
	static long f(long n, int x, int k){ //���-�� ���������� ����� (������� 0), ���������� � ���� ����� �� 0 �� k-1
		if (n == 0)	return 1;
		long b = binpow(10, x - 1);
		long c = n / b;
		return (c < k? c: k)*binpow(k, x - 1) + (c < k? 1: 0)*f(n % b, x - 1, k);
	}
	
	static long fib(int n){
		if (n == 0) return 0;
		if ((n & 1) == 0){
			long f1 = fib(n/2 - 1);
			long f2 = fib(n/2 + 1);
			return f2*f2 - f1*f1;
		}else{
			long f1 = fib(n/2);
			long f2 = fib(n/2 + 1);
			return f1*f1 + f2*f2;
		}
	}
	
	static BigInteger BigFib(int n){
		if (n == 0) return BigInteger.ZERO;
		if ((n & 1) == 0){
			BigInteger f1 = BigFib(n/2 - 1);
			f1 = f1.multiply(f1);
			BigInteger f2 = BigFib(n/2 + 1);
			f2 = f2.multiply(f2);
			return f2.subtract(f1);
		}else{
			BigInteger f1 = BigFib(n/2);
			f1 = f1.multiply(f1);
			BigInteger f2 = BigFib(n/2 + 1);
			f2 = f2.multiply(f2);
			return f2.add(f1);
		}
	}
	
	static public class PointD{
		
		double x, y;
		
		public PointD(double x, double y){
			this.x = x;
			this.y = y;
		}
	}
	
	static double d(Point p1, Point p2){
		return sqrt(d2(p1, p2));
	}
	
	static public double d(PointD p1, PointD p2){
		return sqrt(d2(p1, p2));
	}
	
	static double d2(Point p1, Point p2){
		return (p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y);
	}
	
	static public double d2(PointD p1, PointD p2){
		return (p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y);
	}
	
	static boolean IsProbablyPrime(long n){
		if (n == 1)	return false;
		if ((n & 1) == 0) return false;
		for (int j = 3; j < sqrt(n) + 1; j += 2){
			if (n % j == 0)	return false;
		}
		return true;
	}

	static int[] Sieve(int n){
		boolean[] b = new boolean[n+1];
		Arrays.fill(b, true);
		b[0] = false;
		b[1] = false;
		long nLong = n;
		int j=0;
		for (int i = 1; i <= n; i++) {
			if (b[i]){
				j++;
				if (((long)i)*i <= nLong) {
					for (int k = i*i; k <= n; k += i) {
						b[k] = false;
					}
				}
			}
		}
		int[] p = new int[j];
		Arrays.fill(p, 0);
		j=0;
		for (int i = 2; i <= n; i++) {
			if (b[i]){
				p[j]=i;
				j++;
			}
		}
		return p;
	}
	
	static int[][] Palindromes(String s){
		char[] c = s.toCharArray();
		int n = c.length;
		int[][] d = new int[2][n];
		int l = 0, r = -1;
		for (int i = 0; i < n; i++){
			int j = (i > r? 0: min(d[0][l+r-i+1], r-i+1)) + 1;
			for (; i - j >= 0 && i + j - 1< n && c[i-j] == c[i+j-1]; j++);
			d[0][i] = --j;
			if (i + d[0][i] - 1 > r){
				r = i + d[0][i] - 1;
				l = i - d[0][i];
			}
		}
		l = 0;
		r = -1;
		for (int i = 0; i < n; i++){
			int j = (i > r? 0: min(d[1][l+r-i], r-i)) + 1;
			for (; i - j >= 0 && i + j < n && c[i-j] == c[i+j]; j++);
			d[1][i] = --j;
			if (i + d[1][i] > r){
				r = i + d[1][i];
				l = i - d[1][i];
			}
		}
		return d;
	}
	
	static public class Permutation {
		
		int[] a;
		int n;
		
		public Permutation(int n){
			this.n=n;
			a=new int[n];
			for (int i=0; i<n; i++){
				a[i]=i;
			}
		}
		
		public boolean nextPermutation(){ //������� � do{}while(nextPermutation(a));
			int i=n-1;
			for (i=n-2; i>=0; i--){
				if (a[i]<a[i+1]){
					break;
				}
			}
			if (i==-1){
				return false;
			}
			int jMin=i+1;
			for (int j=n-1; j>i; j--){
				if (a[i]<a[j]&&a[j]<a[jMin]){
					jMin=j;
				}
			}
			swap(i, jMin);
			for (int j=1; j<=(n-i)/2; j++){
				swap(i+j, n-j);
			}
			return true;
		}
		
		
		public int get(int i){
			return a[i];
		}
		
		void swap(int i, int j){
			int r=a[i];
			a[i]=a[j];
			a[j]=r;
		}
	}
	
	static public class Fraction implements Comparable<Fraction>, Cloneable{
		
		public final Fraction FRACTION_ZERO = new Fraction();
		public final Fraction FRACTION_ONE = new Fraction(1);
		public long numerator = 0;
		public long denominator = 1;
		
		public Fraction(){
			numerator = 0;
			denominator = 1;
		}
		
		public Fraction(long numerator){
			this.numerator = numerator;
			denominator = 1;
		}
		
		public Fraction(long numerator, long denominator){
			this.numerator = numerator;
			this.denominator = denominator;
			Cancellation();
		}
		
		public Fraction(double numerator, double denominator, int accuracy){
			this.numerator = (long)(numerator*pow(10,accuracy));
			this.denominator = (long)(denominator*pow(10,accuracy));
			Cancellation();
		}
		
		public Fraction(String s){
			if (s.charAt(0) == '-'){
				denominator = -1;
				s = s.substring(1);
			}
			if (s.indexOf("/") != -1){
				denominator *= Integer.parseInt(s.substring(s.indexOf("/") + 1));
			}
			if (s.indexOf(" ") != -1){
				numerator = Integer.parseInt(s.substring(0, s.indexOf(" "))) * abs(denominator) + Integer.parseInt(s.substring(s.indexOf(" ") + 1, s.indexOf("/")));
			}else{
				if (s.indexOf("/") != -1){
					numerator = Integer.parseInt(s.substring(0, s.indexOf("/")));
				}else{
					numerator = Integer.parseInt(s)*abs(denominator);
				}
			}
			this.Cancellation();
		}
		
		void Cancellation(){
			long g = gcd(abs(numerator), abs(denominator));
			numerator /= g;
			denominator /= g;
			if (denominator < 0){
				numerator *= -1;
				denominator *= -1;
			}
		}
		
		public String toString(){
			String s = "";
			if (numerator == 0){
				return "0";
			}
			if (numerator < 0){
				s += "-";
			}
			if (abs(numerator) >= denominator){
				s += Long.toString(abs(numerator) / denominator) + " ";
			}
			if (abs(numerator) % denominator != 0){
				s += Long.toString(abs(numerator) % denominator);
			}else{
				s = s.substring(0, s.length()-1);
			}
			if (denominator != 1){
				s += "/" + Long.toString(denominator);
			}
			return s;
		}
		
		public Fraction add(Fraction f){
			Fraction fResult = new Fraction();
			fResult.denominator = lcm(denominator, f.denominator);
			fResult.numerator = numerator * fResult.denominator / denominator + f.numerator * fResult.denominator / f.denominator;
			fResult.Cancellation();
			return fResult;
		}
		
		public Fraction subtract(Fraction f){
			Fraction fResult = new Fraction();
			fResult.denominator = lcm(denominator, f.denominator);
			fResult.numerator = numerator * fResult.denominator / denominator - f.numerator * fResult.denominator / f.denominator;
			fResult.Cancellation();
			return fResult;
		}
		
		public Fraction multiply(Fraction f){
			Fraction fResult = new Fraction();
			fResult.numerator = numerator * f.numerator;
			fResult.denominator = denominator * f.denominator;
			fResult.Cancellation();
			return fResult;
		}
		
		public Fraction divide(Fraction f){
			Fraction fResult = new Fraction();
			fResult.numerator = numerator * f.denominator;
			fResult.denominator = denominator * f.numerator;
			fResult.Cancellation();
			return fResult;
		}
		
		@Override
		public int compareTo(Fraction f){
			long g = gcd(denominator, f.denominator);
			long res = numerator * (f.denominator / g) - f.numerator * (denominator / g);
			if (res < 0){
				return -1;
			}
			if (res > 0){
				return 1;
			}
			return 0;
		}
		
		public Fraction clone(){
			Fraction fResult = new Fraction(numerator, denominator);
			return fResult;
		}
		
		public Fraction floor(){
			Fraction fResult = this.clone();
			fResult.numerator = (fResult.numerator / fResult.denominator) * fResult.denominator;
			return fResult;
		}
		
		public Fraction ceil(){
			Fraction fResult = this.clone();
			fResult.numerator = (fResult.numerator/fResult.denominator + 1) * fResult.denominator;
			return fResult;
		}
		
		public Fraction binpow(int n){
			if (n==0) return FRACTION_ONE;
			if ((n&1)==0){
				Fraction f=this.binpow(n/2);
				return f.multiply(f);
			}else return binpow(n-1).multiply(this);
		}
	}
	
	static public class FenwickTree_1{	//One-dimensional array		
		
		int n;
		long[] t;
		
		public FenwickTree_1(int n){
			this.n = n;
			t = new long[n];
		}
		
		public long sum(int xl, int xr){
			return sum(xr) - sum(xl);
		}
		
		public long sum(int x){
			long result = 0;
			for (int i = x; i >= 0; i = (i & (i + 1)) - 1){
				result += t[i];
			}
			return result;
		}
		
		public void update(int x, long delta){
			for (int i = x; i < n; i = (i | (i + 1))){
				t[i] += delta;
			}
		}
	}
	
	static public class FenwickTree_2{	//Two-dimensional array
		
		int n, m;
		long[][] t;
		
		public FenwickTree_2(int n, int m){
			this.n = n;
			this.m = m;
			t = new long[n][m];
		}
		
		public long sum(int xl, int yl, int xr, int yr){
			return sum(xr, yr) - sum(xl - 1, yr) - sum(xr, yl - 1) + sum(xl - 1, yl - 1);
		}
		
		public long sum(int x, int y){
			long result = 0;
			for (int i = x; i >= 0; i = (i & (i + 1)) - 1){
				for (int j = y; j >= 0; j = (j & (j + 1)) - 1){
					result+=t[i][j];
				}
			}
			return result;
		}
		
		public void update(int x, int y, long delta){
			for (int i = x; i < n; i = (i | (i + 1))){
				for (int j = y; j < m; j = (j | (j + 1))){
					t[i][j] += delta;
				}
			}
		}
	}
	
	static public class FenwickTree_3{	//Three-dimensional array
		
		int n, m, l;
		long[][][] t;
		
		public FenwickTree_3(int n, int m, int l){
			this.n = n;
			this.m = m;
			this.l = l;
			t = new long[n][m][l];
		}
		
		public long sum(int xl, int yl, int zl, int xr, int yr, int zr){
			return sum(xr, yr, zr) - sum(xl - 1, yr, zr)
			+ sum(xl - 1, yr, zl - 1) - sum(xr, yr, zl - 1)
			- sum(xr, yl - 1, zr) + sum(xl - 1, yl - 1, zr)
			- sum(xl - 1, yl - 1, zl - 1) + sum(xr, yl - 1, zl - 1);
		}
		
		public long sum(int x, int y, int z){
			long result = 0;
			for (int i = x; i >= 0; i = (i & (i + 1)) - 1){
				for (int j = y; j >= 0; j = (j & (j + 1)) - 1){
					for (int k = z; k >= 0; k = (k & (k + 1)) - 1){
						result += t[i][j][k];
					}
				}
			}
			return result;
		}
		
		public void update(int x, int y, int z, long delta){
			for (int i = x; i < n; i = (i | (i + 1))){
				for (int j = y; j < n; j = (j | (j + 1))){
					for (int k = z; k < n; k = (k | (k + 1))){
						t[i][j][k] += delta;
					}
				}
			}
		}
	}
}