Calculate the minimum number of characters you need to change in the string s, so that it contains at least k different letters, or print that it is impossible.

String s consists only of lowercase Latin letters, and it is allowed to change characters only to lowercase Latin letters too.

Input

First line of input contains string s, consisting only of lowercase Latin letters (1 ≤ |s| ≤ 1000, |s| denotes the length of s).

Second line of input contains integer k (1 ≤ k ≤ 26).

Output

Print single line with a minimum number of necessary changes, or the word «impossible» (without quotes) if it is impossible.

Examples

Input

yandex
6


Output

0


Input

yahoo
5


Output

1


Input

google
7


Output

impossible

Note

In the first test case string contains 6 different letters, so we don't need to change anything.

In the second test case string contains 4 different letters: {'a', 'h', 'o', 'y'}. To get 5 different letters it is necessary to change one occurrence of 'o' to some letter, which doesn't occur in the string, for example, {'b'}.

In the third test case, it is impossible to make 7 different letters because the length of the string is 6.
import java.util.ArrayList;
import java.util.InputMismatchException;
import java.util.Locale;
import java.util.Scanner;
import java.util.regex.Pattern;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.UnsupportedEncodingException;

 
 
public class Main {
	
	
	public static void main(String[] args) throws Exception {
        solve(1);	
    }
 
    
    public static void solve(int testCases) throws Exception{
    	
    	String s = StdIn.readString();
    	int k = StdIn.readInt();
    	
    	if(k > s.length()){
    		StdOut.println("impossible");
    		return;
    	}
    	
    	boolean[] f = new boolean[26];
    	int count = 0;
    	for(int i = 0 ; i < s.length() ; i++){
    		if(!f[s.charAt(i)-'a']){
    			count++;
    			f[s.charAt(i)-'a'] = true;
    		}
    	}
    	if(count > k)
    		StdOut.println(0);
    	else
    		StdOut.println(k-count);
    }
}


final class StdIn {
 
    private StdIn() { }
 
    private static Scanner scanner;
    
    private static final String CHARSET_NAME = "UTF-8";
 
    private static final Locale LOCALE = Locale.US;
 
    private static final Pattern WHITESPACE_PATTERN = Pattern.compile("\\p{javaWhitespace}+");
 
    private static final Pattern EMPTY_PATTERN = Pattern.compile("");
 
    private static final Pattern EVERYTHING_PATTERN = Pattern.compile("\\A");
 
    public static boolean isEmpty() {
        return !scanner.hasNext();
    }
 
    public static boolean hasNextLine() {
        return scanner.hasNextLine();
    }
 
    public static boolean hasNextChar() {
        scanner.useDelimiter(EMPTY_PATTERN);
        boolean result = scanner.hasNext();
        scanner.useDelimiter(WHITESPACE_PATTERN);
        return result;
    }
 
    public static String readLine() {
        String line;
        try                 { line = scanner.nextLine(); }
        catch (Exception e) { line = null;               }
        return line;
    }
 
    public static char readChar() {
        scanner.useDelimiter(EMPTY_PATTERN);
        String ch = scanner.next();
        assert (ch.length() == 1) : "Internal (Std)In.readChar() error!"
            + " Please contact the authors.";
        scanner.useDelimiter(WHITESPACE_PATTERN);
        return ch.charAt(0);
    }  
 
 
    public static String readAll() {
        if (!scanner.hasNextLine())
            return "";
 
        String result = scanner.useDelimiter(EVERYTHING_PATTERN).next();
        // not that important to reset delimeter, since now scanner is empty
        scanner.useDelimiter(WHITESPACE_PATTERN); // but let's do it anyway
        return result;
    }
 
    public static String readString() {
        return scanner.next();
    }
 
    public static int readInt() {
        return scanner.nextInt();
    }
 
    public static double readDouble() {
        return scanner.nextDouble();
    }
 
    public static float readFloat() {
        return scanner.nextFloat();
    }
 
    public static long readLong() {
        return scanner.nextLong();
    }
    
    public static short readShort() {
        return scanner.nextShort();
    }
 
    public static byte readByte() {
        return scanner.nextByte();
    }
 
    public static boolean readBoolean() {
        String s = readString();
        if (s.equalsIgnoreCase("true"))  return true;
        if (s.equalsIgnoreCase("false")) return false;
        if (s.equals("1"))               return true;
        if (s.equals("0"))               return false;
        throw new InputMismatchException();
    }
 
    public static String[] readAllStrings() {
        // we could use readAll.trim().split(), but that's not consistent
        // because trim() uses characters 0x00..0x20 as whitespace
        String[] tokens = WHITESPACE_PATTERN.split(readAll());
        if (tokens.length == 0 || tokens[0].length() > 0)
            return tokens;
 
        // don't include first token if it is leading whitespace
        String[] decapitokens = new String[tokens.length-1];
        for (int i = 0; i < tokens.length - 1; i++)
            decapitokens[i] = tokens[i+1];
        return decapitokens;
    }
 
    public static String[] readAllLines() {
        ArrayList<String> lines = new ArrayList<String>();
        while (hasNextLine()) {
            lines.add(readLine());
        }
        return lines.toArray(new String[0]);
    }
 
    public static int[] readAllInts() {
        String[] fields = readAllStrings();
        int[] vals = new int[fields.length];
        for (int i = 0; i < fields.length; i++)
            vals[i] = Integer.parseInt(fields[i]);
        return vals;
    }
 
    public static double[] readAllDoubles() {
        String[] fields = readAllStrings();
        double[] vals = new double[fields.length];
        for (int i = 0; i < fields.length; i++)
            vals[i] = Double.parseDouble(fields[i]);
        return vals;
    }
    
    static {
        resync();
    }
 
    private static void resync() {
        setScanner(new Scanner(new java.io.BufferedInputStream(System.in), CHARSET_NAME));
    }
    
    private static void setScanner(Scanner scanner) {
        StdIn.scanner = scanner;
        StdIn.scanner.useLocale(LOCALE);
    }
 
    public static int[] readInts() {
        return readAllInts();
    }
 
    public static double[] readDoubles() {
        return readAllDoubles();
    }
 
    public static String[] readStrings() {
        return readAllStrings();
    }
 
}
 
final class StdOut {
 
    private static final String CHARSET_NAME = "UTF-8";
 
    private static final Locale LOCALE = Locale.US;
 
    private static PrintWriter out;
 
    static {
        try {
            out = new PrintWriter(new OutputStreamWriter(System.out, CHARSET_NAME), true);
        }
        catch (UnsupportedEncodingException e) { System.out.println(e); }
    }
 
    private StdOut() { }
 
    public static void close() {
        out.close();
    }
 
    public static void println() {
        out.println();
    }
 
    public static void println(Object x) {
        out.println(x);
    }
 
    public static void println(boolean x) {
        out.println(x);
    }
 
    public static void println(char x) {
        out.println(x);
    }
 
    public static void println(double x) {
        out.println(x);
    }
 
    public static void println(float x) {
        out.println(x);
    }
 
    public static void println(int x) {
        out.println(x);
    }
 
    public static void println(long x) {
        out.println(x);
    }
 
    public static void println(short x) {
        out.println(x);
    }
 
    public static void println(byte x) {
        out.println(x);
    }
 
    public static void print() {
        out.flush();
    }
 
    public static void print(Object x) {
        out.print(x);
        out.flush();
    }
 
    public static void print(boolean x) {
        out.print(x);
        out.flush();
    }
 
    public static void print(char x) {
        out.print(x);
        out.flush();
    }
 
    public static void print(double x) {
        out.print(x);
        out.flush();
    }
 
    public static void print(float x) {
        out.print(x);
        out.flush();
    }
 
    public static void print(int x) {
        out.print(x);
        out.flush();
    }
 
    public static void print(long x) {
        out.print(x);
        out.flush();
    }
 
    public static void print(short x) {
        out.print(x);
        out.flush();
    }
 
    public static void print(byte x) {
        out.print(x);
        out.flush();
    }
 
    public static void printf(String format, Object... args) {
        out.printf(LOCALE, format, args);
        out.flush();
    }
 
    public static void printf(Locale locale, String format, Object... args) {
        out.printf(locale, format, args);
        out.flush();
    }
 
} 