Problem: Piegirl is buying stickers for a project. Stickers come on sheets, and each sheet of stickers contains exactly n stickers. Each sticker has exactly one character printed on it, so a sheet of stickers can be described by a string of length n. Piegirl wants to create a string s using stickers. She may buy as many sheets of stickers as she wants, and may specify any string of length n for the sheets, but all the sheets must be identical, so the string is the same for all sheets. Once she attains the sheets of stickers, she will take some of the stickers from the sheets and arrange (in any order) them to form s. Determine the minimum number of sheets she has to buy, and provide a string describing a possible sheet of stickers she should buy.

Input

The first line contains string s (1 ≤ |s| ≤ 1000), consisting of lowercase English characters only. The second line contains an integer n (1 ≤ n ≤ 1000).

Output

On the first line, print the minimum number of sheets Piegirl has to buy. On the second line, print a string consisting of n lower case English characters. This string should describe a sheet of stickers that Piegirl can buy in order to minimize the number of sheets. If Piegirl cannot possibly form the string s, print instead a single line with the number -1.

Examples

Input

banana
4


Output

2
baan


Input

banana
3


Output

3
nab


Input

banana
2


Output

-1

Note

In the second example, Piegirl can order 3 sheets of stickers with the characters "nab". She can take characters "nab" from the first sheet, "na" from the second, and "a" from the third, and arrange them to from "banana".

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.math.*;

final public class Main implements Runnable {
	private static boolean local;

	public static void main(String[] args) {
		if (args.length > 0 && args[0].equals("-1")) {
			local = true;
		}
		new Thread(null, new Main(), "mainthread", 1 << 27).start();
	}

	public void run() {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;

		try {
			if (local) {
				inputStream = new FileInputStream("/home/outside/coding/workspace/java/main/io/input.txt");
				outputStream = new FileOutputStream("/home/outside/coding/workspace/java/main/io/output.txt");
			} else {
				// inputStream = new FileInputStream("file_name");
				// outputStream = new FileOutputStream("file_name");
			}
		} catch (Exception e) {
			throw new RuntimeException(e);
		}

		Task.in = new InputReader(inputStream);
		Task.out = new OutputWriter(outputStream);
		if (local) {
			Task.dout = new DebugWriter(Task.out);
		}
		
		new Task().solve();
		Task.out.close();
	}
}

final class Task {
	public static InputReader in;
	public static OutputWriter out;
	public static DebugWriter dout;
	
	public void solve() {
		mas = new int[SZ];
		char[] s = in.readString().toCharArray();
		for (int i = 0; i < s.length; ++i)
			++mas[s[i] - 'a'];
		
		int n = in.readInt();
		
		dp = new int[SZ][n + 1];
		was = new boolean[SZ][n + 1];
		
		// dout.printLine(mas);
		int res = f(0,n);
		if (res == INF) {
			out.printLine(-1);
		} else {
			out.printLine(res);
			ans = new ArrayList<>();
			dfs(0, n);
			for (int i = 0; i < ans.size(); ++i)
				out.print((char)(ans.get(i) + 'a'));
			out.printLine();
		}
	}
	
	final int INF = Integer.MAX_VALUE;
	final int SZ = 26;
	int[] mas;
	int[][] dp;
	boolean[][] was;
	int f(int let, int n) {
		if (let == SZ) {
			if (n == 0) {
				return 0;
			} else {
				return INF;
			}
		}
		
		if (was[let][n]) return dp[let][n];
		was[let][n] = true;
		
		if (mas[let] == 0)
			return dp[let][n] = f(let + 1, n);
			
		int res = INF;
		
		for (int i = 1; i <= n; ++i) {
			int value = f(let + 1, n - i);
			
			if (value != INF) {
				value = Math.max(value, (mas[let] + i - 1) / i);
				res = Math.min(res, value);
			}
		}
		
		return dp[let][n] = res;
	}
	
	ArrayList<Integer> ans;
	
	void dfs(int let, int n) {
		if (let == SZ) return;
		
		if (mas[let] == 0) {
			dfs(let + 1, n);
			return;
		}
		
		for (int i = 1; i <= n; ++i) {
			int value = f(let + 1, n - i);
			
			if (value != INF) {
				value = Math.max(value, (mas[let] + i - 1) / i);
				
				if (value == f(let, n)) {
					for (int k = 0; k < i; ++k)
						ans.add(let);
					dfs(let + 1, n - i);
					return;
				}
			}
		}
	}
}

final class InputReader {
	private boolean finished = false;

	private InputStream stream;
	private byte[] buf = new byte[1 << 13];
	private int curChar;
	private int numChars;

	public InputReader(InputStream stream) {
		this.stream = stream;
	}

	private int read() {
		if (numChars == -1)
			throw new InputMismatchException();
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			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 int readInt() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	public long readLong() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	public String readString() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}

	public static boolean isSpaceChar(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

	private String readLine0() {
		StringBuilder buf = new StringBuilder();
		int c = read();
		while (c != '\n' && c != -1) {
			if (c != '\r')
				buf.appendCodePoint(c);
			c = read();
		}
		return buf.toString();
	}

	public String readLine() {
		String s = readLine0();
		while (s.trim().length() == 0)
			s = readLine0();
		return s;
	}

	public String readLine(boolean ignoreEmptyLines) {
		if (ignoreEmptyLines)
			return readLine();
		else
			return readLine0();
	}
	
	public String readToEnd() {
		StringBuilder buf = new StringBuilder();
		int c = read();
		while (c != -1) {
			if (c != '\r')
				buf.appendCodePoint(c);
			c = read();
		}
		return buf.toString();
	}

	public BigInteger readBigInteger() {
		try {
			return new BigInteger(readString());
		} catch (NumberFormatException e) {
			throw new InputMismatchException();
		}
	}

	public char readCharacter() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		return (char) c;
	}

	public double readDouble() {
		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, readInt());
			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, readInt());
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				m /= 10;
				res += (c - '0') * m;
				c = read();
			}
		}
		return res * sgn;
	}

	public boolean isExhausted() {
		int value;
		while (isSpaceChar(value = peek()) && value != -1)
			read();
		return value == -1;
	}
	
	public void close() {
		try {
			stream.close();
		} catch (IOException e) {
			throw new RuntimeException();           
		}
	}
}

final class OutputWriter {
	private final PrintWriter writer;

	public OutputWriter(OutputStream outputStream) {
		writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream), 1 << 13));
	}

	public OutputWriter(Writer writer) {
		this.writer = new PrintWriter(writer);
	}


	public void print(Object... objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(Object... objects) {
		print(objects);
		writer.println();
	}

	public void printFormat(String format, Object... objects) {
		writer.printf(format, objects);
	}


	public void print(char[] objects) {
		writer.print(objects);
	}

	public void printLine(char[] objects) {
		writer.println(objects);
	}

	public void printLine(char[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void print(int[] objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(int[] objects) {
		print(objects);
		writer.println();
	}

	public void printLine(int[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void print(short[] objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(short[] objects) {
		print(objects);
		writer.println();
	}

	public void printLine(short[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void print(long[] objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(long[] objects) {
		print(objects);
		writer.println();
	}

	public void printLine(long[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void print(double[] objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(double[] objects) {
		print(objects);
		writer.println();
	}

	public void printLine(double[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void print(byte[] objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(byte[] objects) {
		print(objects);
		writer.println();
	}

	public void printLine(byte[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void print(boolean[] objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(boolean[] objects) {
		print(objects);
		writer.println();
	}

	public void printLine(boolean[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void close() {
		writer.close();
	}

	public void flush() {
		writer.flush();
	}
}

final class DebugWriter {
	private final OutputWriter writer;

	public DebugWriter(OutputWriter writer) {
		this.writer = writer;
	}

	private void printDebugMessage() {
		writer.print("DEBUG:\t");
	}

	public void printLine(Object... objects) {
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printFormat(String format, Object... objects) {
		printDebugMessage();
		writer.printFormat(format, objects);
		flush();
	}

	public void printLine(char[] objects) {
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(char[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}

	public void printLine(double[] objects) {
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(double[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}

	public void printLine(int[] objects) {
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(int[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}

	public void printLine(short[] objects) {
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(short[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}

	public void printLine(long[] objects) {
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(long[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}

	public void printLine(byte[] objects) {
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(byte[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}

	public void printLine(boolean[] objects) {
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(boolean[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}

	public void flush() {
		writer.flush();
	}
}