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.*;
import java.io.*;

public class AIMTECH4A {
	public static void main(String args[]) {
		InputReader in = new InputReader(System.in);
		OutputStream outputStream = System.out;
		PrintWriter out = new PrintWriter(outputStream);
		/*------------------------------My Code starts here------------------------------*/
		String s=in.next();
		int i,k=in.nextInt();
		Set<Character> st=new HashSet<>();
		for(i=0;i<s.length();i++)
			st.add(s.charAt(i));
		if(st.size()>=k)
			out.println(0);
		else if(k>s.length())
			out.println("impossible");
		else
			out.println(k-st.size());
		out.close();
		/*------------------------------The End------------------------------------------*/
	}

	public static final long l = (int) (1e9 + 7);

	private static int[] nextIntArray(InputReader in, int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = in.nextInt();
		return a;
	}

	private static long[] nextLongArray(InputReader in, int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = in.nextLong();
		return a;
	}

	private static int[][] nextIntMatrix(InputReader in, int n, int m) {
		int[][] a = new int[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++)
				a[i][j] = in.nextInt();
		}
		return a;
	}

	private static void show(int[] a) {
		for (int i = 0; i < a.length; i++)
			System.out.print(a[i] + " ");
		System.out.println();
	}

	private static void show2DArray(char[][] a) {
		for (int i = 0; i < a.length; i++) {
			for (int j = 0; j < a[0].length; j++)
				System.out.print(a[i][j]);
			System.out.println();
		}
	}

	static class Pair {
		private int first;
		private int second;

		public Pair(int i, int j) {
			this.first = i;
			this.second = j;
		}

		public int getFirst() {
			return first;
		}

		public int getSecond() {
			return second;
		}

		public void setFirst(int k) {
			this.first = k;
		}

		public void setSecond(int k) {
			this.second = k;
		}
	}

	static int modPow(int a, int b, int p) {
		int result = 1;
		a %= p;
		while (b > 0) {
			if ((b & 1) != 0)
				result = (result * a) % p;
			b = b >> 1;
			a = (a * a) % p;
		}
		return result;
	}

	public static void SieveOfEratosthenes(int n) {
		boolean[] prime = new boolean[n + 1];
		Arrays.fill(prime, true);
		prime[1] = false;
		int i, j;
		for (i = 2; i * i <= n; i++) {
			if (prime[i]) {
				for (j = i; j <= n; j += i) {
					if (j != i)
						prime[j] = false;
				}
			}
		}
	}

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream inputstream) {
			reader = new BufferedReader(new InputStreamReader(inputstream));
			tokenizer = null;
		}

		public String nextLine() {
			String fullLine = null;
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					fullLine = reader.readLine();
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
				return fullLine;
			}
			return fullLine;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}
	}

}
