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.io.IOException;

public class Main
{
    static class Scan
    {
        final private int BUF_SIZE = 1 << 16;
        private int cur_size = 0;
        private int pointer = 0;
        private java.io.DataInputStream in;
        private byte buffer[] = new byte[BUF_SIZE];

        Scan(java.io.InputStream input)
        {
            in = new java.io.DataInputStream(input);
        }

        // fills the buffer with characters
        private void fill() throws java.io.IOException
        {
            cur_size = in.read(buffer, 0, BUF_SIZE);
            if (cur_size == -1) buffer[0] = 0;
            pointer = 0;
        }

        private byte read() throws java.io.IOException
        {
            if (pointer == cur_size) fill();
            return buffer[pointer++];
        }

        int readInt() throws java.io.IOException
        {
            int res = 0;
            byte c;
            while ((c = read()) <= ' ');
            boolean negate = c == '-';
            if (negate) c = read();
            while (c >= '0' && c <= '9')
            {
                res = res * 10 + c - '0';
                c = read();
            }
            return negate ? -res : res;
        }

        long readLong() throws java.io.IOException
        {
            long res = 0;
            byte c;
            while ((c = read()) <= ' ') ;
            boolean negate = c == '-';
            if (negate) c = read();
            while (c >= '0' && c <= '9') {
                res = res * 10 + c - '0';
                c = read();
            }
            return negate ? -res : res;
        }

        double readDouble() throws java.io.IOException
        {
            byte c;
            while ((c = read()) <= ' ');
            boolean negate = c == '-';
            if (negate)
                c = read();
            int power = 0;
            long res = 0;
            boolean dot_flag = false;
            for (;(c >= '0' && c <= '9') || c == '.'; c = read())
            {
                if (dot_flag)
                    power++;
                if (c == '.')
                    dot_flag = true;
                else
                    res = res * 10 + c - '0';
            }
            double ret = res / Math.pow(10, power);
            return negate ? -ret : ret;
        }

        // skip defines whether ' ', '\n', '\r' must be skipped in readChar method
        char readChar(boolean skip) throws java.io.IOException
        {
            if (skip)
            {
                byte c;
                while ((c = read()) == ' ' || c == '\n' || c == '\r');
                return (char) c;
            }
            return (char) read();
        }

        // skip defines whether current string must be skipped in readString and readText methods

        /* If exact length is known, in terms of efficiency
         it is better to specify it while using readText, readString and readWord methods */

        String readWord() throws java.io.IOException
        {
            byte c;
            while ((c = read()) == '\n' || c == ' ' || c == '\r');
            StringBuilder s = new StringBuilder();
            s.append((char)c);
            for (;(c = read()) != '\n' && c != ' ' && c != '\r' && c != 0; s.append((char)c));
            return s.toString();
        }

        String readWord(int LEN) throws java.io.IOException
        {
            byte[] s = new byte[LEN];
            byte c;
            while ((c = read()) == '\n' || c == ' ' || c == '\r');
            s[0] = c;
            for (int i = 1; (c = read()) != ' ' && c != '\n' && c != '\r' && c != 0; s[i++] = c);
            return new String(s);
        }

        String readString(boolean skip, int LEN) throws java.io.IOException
        {
            byte[] s = new byte[LEN];
            byte c;
            if (skip)
                while ((c = read()) != '\n');
            for (int i = 0; (c = read()) != '\n' && c != '\r' && c != 0; s[i++] = c);
            read();
            return new String(s);
        }

        String readString(boolean skip) throws java.io.IOException
        {
            StringBuilder s = new StringBuilder("");
            byte c;
            if (skip)
                while ((c = read()) != '\n');
            for (;(c = read()) != '\n' && c != '\r' && c != 0; s.append((char)c));
            read();
            return s.toString();
        }

        String readText(boolean skip, int LEN) throws java.io.IOException
        {
            byte[] s = new byte[LEN];
            byte c;
            if (skip)
                while ((c = read()) != '\n');
            for (int i = 0; (c = read()) != 0; s[i++] = c);
            return new String(s);
        }

        String readText(boolean skip) throws java.io.IOException
        {
            StringBuilder s = new StringBuilder("");
            byte c;
            if (skip)
                while ((c = read()) != '\n');
            for (;(c = read()) != 0; s.append((char)c));
            return s.toString();
        }
    }

    public static void main(String[] args) throws IOException
    {
        Scan in = new Scan(System.in);
        String s = in.readWord();
        int n = in.readInt();
        if (n > s.length())
        {
            System.out.println("impossible");
            return;
        }
        int cnt[] = new int[26];
        int res = 0;
        for (int i = 0; i < s.length(); i++)
        {
            if (cnt[s.charAt(i) - 'a'] == 0)
                res++;
            cnt[s.charAt(i) - 'a']++;
        }
        System.out.println(Math.max(0, n - res));
    }
}
