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.*;
import java.lang.Math.*;

public class MainA {

	
	static int mod = (int) 1e9 + 7;

	public static void main(String[] args) {

		InputReader in = new InputReader(System.in);
		PrintWriter out = new PrintWriter(System.out);
		String s=in.nextLine();
		int k=in.nextInt();
		int a[]=new int[26];int count=0;
		for(int i=0;i<s.length();i++)
		{
			if(a[s.charAt(i)-'a']==0)count++;
			a[s.charAt(i)-'a']++;
		}
		int rem=s.length()-count;
		if(count>=k)out.println(0);
		else
		{
			if(rem<k-count)out.println("impossible");
			else out.println(k-count);
		}
		out.close();
	}

	static class Pairs implements Comparable<Pairs> {
		int x;
		int y;

		Pairs(int a, int b) {
			x = a;
			y = b;
		}

		@Override
		public int compareTo(Pairs o) {
			// TODO Auto-generated method stub
			if (x == o.x)
				return Integer.compare(y, o.y);
			else
				return Long.compare(x, o.x);
		}

	}

	public static void debug(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}

	public static boolean isPal(String s) {
		for (int i = 0, j = s.length() - 1; i <= j; i++, j--) {
			if (s.charAt(i) != s.charAt(j))
				return false;
		}
		return true;
	}

	public static String rev(String s) {
		StringBuilder sb = new StringBuilder(s);
		sb.reverse();
		return sb.toString();
	}

	public static long gcd(long x, long y) {
		if (y == 0)
			return x;
		if (x % y == 0)
			return y;
		else
			return gcd(y, x % y);
	}

	public static int gcd(int x, int y) {
		if (x % y == 0)
			return y;
		else
			return gcd(y, x % y);
	}

	public static long gcdExtended(long a, long b, long[] x) {

		if (a == 0) {
			x[0] = 0;
			x[1] = 1;
			return b;
		}
		long[] y = new long[2];
		long gcd = gcdExtended(b % a, a, y);

		x[0] = y[1] - (b / a) * y[0];
		x[1] = y[0];

		return gcd;
	}

	public static int abs(int a, int b) {
		return (int) Math.abs(a - b);
	}

	public static long abs(long a, long b) {
		return (long) Math.abs(a - b);
	}

	public static int max(int a, int b) {
		if (a > b)
			return a;
		else
			return b;
	}

	public static int min(int a, int b) {
		if (a > b)
			return b;
		else
			return a;
	}

	public static long max(long a, long b) {
		if (a > b)
			return a;
		else
			return b;
	}

	public static long min(long a, long b) {
		if (a > b)
			return b;
		else
			return a;
	}

	public static long[][] mul(long a[][], long b[][]) {
		long c[][] = new long[2][2];
		c[0][0] = a[0][0] * b[0][0] + a[0][1] * b[1][0];
		c[0][1] = a[0][0] * b[0][1] + a[0][1] * b[1][1];
		c[1][0] = a[1][0] * b[0][0] + a[1][1] * b[1][0];
		c[1][1] = a[1][0] * b[0][1] + a[1][1] * b[1][1];

		return c;
	}

	public static long pow(long n, long p,long m) {
		long result = 1;
		if (p == 0)
			return 1;
		if (p == 1)
			return n;
		while (p != 0) {
			if (p % 2 == 1)
				result =(result*n)%m;
			p >>= 1;
			n=(n*n)%m;
		}
		return result;
	}

	static class InputReader {

		private final InputStream stream;
		private final byte[] buf = new byte[8192];
		private int curChar, snumChars;
		private SpaceCharFilter filter;

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

		public int snext() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

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

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

		public int[] nextIntArray(int n) {
			int a[] = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = nextInt();
			}
			return a;
		}

		public long[] nextLongArray(int n) {
			long a[] = new long[n];
			for (int i = 0; i < n; i++) {
				a[i] = nextInt();
			}
			return a;
		}

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

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

		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}
}