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.PrintWriter;
import java.util.*;
import java.util.function.Predicate;

public class TP {

    public static PrintWriter out = new PrintWriter(System.out);
    public static Scanner in = new Scanner(System.in);

    public static void main(String[] args) {
        long s = System.currentTimeMillis();
        int t = 1;
//        t = ni();
        while (t-- > 0) solve();
        out.flush();
        tr(System.currentTimeMillis() - s + "ms");
    }

    private static void solve() {
//        char[] s = in.next().toCharArray();
        String s = in.next();
        int k = ni();
        int n = s.length();
        if (n < k) {
            System.out.println("impossible");
            return;
        }
        HashSet<Character> set = new HashSet<>();
        for (char c : s.toCharArray()) set.add(c);
        System.out.println(Math.max(0, k - set.size()));
    }

    private static boolean ch1(char[] s) {
        boolean ok = true;
        for (char c : s) ok = ok && Character.isUpperCase(c);
        return ok;
    }


    private static boolean ch2(char[] s) {
        boolean ok = Character.isLowerCase(s[0]);
        for (int i = 1; i < s.length; i++) ok = ok && Character.isUpperCase(s[i]);
        return ok;
    }


    private static long lcm(long a, long b) {
        return a * b / gcd(a, b);
    }

    public static int[][] enumPrimesAndLPF(int n) {
        int[] lpf = new int[n + 1];
        double lu = Math.log(n + 32);

        int tot = 0;
        int[] primes = new int[(int) ((n + 32) / lu + (n + 32) / lu / lu * 1.5)];

        for (int i = 2; i <= n; i++) {
            lpf[i] = i;
        }

        for (int p = 2, tmp; p <= n; p++) {
            if (lpf[p] == p) {
                primes[tot++] = p;
            }
            for (int i = 0; i < tot && primes[i] <= lpf[p] && (tmp = primes[i] * p) <= n; i++) {
                lpf[tmp] = primes[i];
            }
        }

        return new int[][]{Arrays.copyOf(primes, tot), lpf};
    }

    static boolean isPrime(int n) {
        for (int i = 2; i * i <= n; i++) if (n % i == 0) return false;
        return true;
    }

    static boolean sorted(int[] a) {
        for (int i = 0; i < a.length - 1; i++) {
            if (a[i] > a[i + 1]) return false;
        }
        return true;
    }

    public static long gcd(long a, long b) {
        while (b != 0) {
            a %= b;
            long t = a;
            a = b;
            b = t;
        }
        return a;
    }

    private static int ni() {
        return in.nextInt();
    }

    private static int[] na(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = ni();
        return a;
    }

    private static long[] nal(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) a[i] = nl();
        return a;
    }

    private static long nl() {
        return in.nextLong();
    }

    private float nf() {
        return in.nextFloat();
    }

    private static double nd() {
        return in.nextDouble();
    }

    public static int[] facs(int n, int[] primes) {
        int[] ret = new int[9];
        int rp = 0;
        for (int p : primes) {
            if (p * p > n) break;
            int i;
            i = 0;
            while (n % p == 0) {
                n /= p;
                i++;
            }
            if (i > 0) ret[rp++] = p;
        }
        if (n != 1) ret[rp++] = n;
        return Arrays.copyOf(ret, rp);
    }

    public static int[] sieveEratosthenes(int n) {
        if (n <= 32) {
            int[] primes = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31};
            for (int i = 0; i < primes.length; i++) {
                if (n < primes[i]) {
                    return Arrays.copyOf(primes, i);
                }
            }
            return primes;
        }

        int u = n + 32;
        double lu = Math.log(u);
        int[] ret = new int[(int) (u / lu + u / lu / lu * 1.5)];
        ret[0] = 2;
        int pos = 1;

        int[] isnp = new int[(n + 1) / 32 / 2 + 1];
        int sup = (n + 1) / 32 / 2 + 1;

        int[] tprimes = {3, 5, 7, 11, 13, 17, 19, 23, 29, 31};
        for (int tp : tprimes) {
            ret[pos++] = tp;
            int[] ptn = new int[tp];
            for (int i = (tp - 3) / 2; i < tp << 5; i += tp) ptn[i >> 5] |= 1 << (i & 31);
            for (int j = 0; j < sup; j += tp) {
                for (int i = 0; i < tp && i + j < sup; i++) {
                    isnp[j + i] |= ptn[i];
                }
            }
        }

        // 3,5,7
        // 2x+3=n
        int[] magic = {
                0, 1, 23, 2, 29, 24, 19, 3, 30, 27, 25, 11, 20, 8, 4, 13, 31, 22, 28, 18, 26, 10, 7, 12, 21,
                17, 9, 6, 16, 5, 15, 14
        };
        int h = n / 2;
        for (int i = 0; i < sup; i++) {
            for (int j = ~isnp[i]; j != 0; j &= j - 1) {
                int pp = i << 5 | magic[(j & -j) * 0x076be629 >>> 27];
                int p = 2 * pp + 3;
                if (p > n) break;
                ret[pos++] = p;
                if ((long) p * p > n) continue;
                for (int q = (p * p - 3) / 2; q <= h; q += p) isnp[q >> 5] |= 1 << q;
            }
        }

        return Arrays.copyOf(ret, pos);
    }


    private static boolean oj = System.getProperty("ONLINE_JUDGE") != null;

    private static void tr(Object... o) {
        if (!oj) System.out.println(Arrays.deepToString(o));
    }
}


