And where the are the phone numbers?

You are given a string s consisting of lowercase English letters and an integer k. Find the lexicographically smallest string t of length k, such that its set of letters is a subset of the set of letters of s and s is lexicographically smaller than t.

It's guaranteed that the answer exists.

Note that the set of letters is a set, not a multiset. For example, the set of letters of abadaba is {a, b, d}.

String p is lexicographically smaller than string q, if p is a prefix of q, is not equal to q or there exists i, such that pi < qi and for all j < i it is satisfied that pj = qj. For example, abc is lexicographically smaller than abcd , abd is lexicographically smaller than abec, afa is not lexicographically smaller than ab and a is not lexicographically smaller than a.

Input

The first line of input contains two space separated integers n and k (1 ≤ n, k ≤ 100 000) — the length of s and the required length of t.

The second line of input contains the string s consisting of n lowercase English letters.

Output

Output the string t conforming to the requirements above.

It's guaranteed that the answer exists.

Examples

Input

3 3
abc


Output

aca


Input

3 2
abc


Output

ac


Input

3 3
ayy


Output

yaa


Input

2 3
ba


Output

baa

Note

In the first example the list of strings t of length 3, such that the set of letters of t is a subset of letters of s is as follows: aaa, aab, aac, aba, abb, abc, aca, acb, .... Among them, those are lexicographically greater than abc: aca, acb, .... Out of those the lexicographically smallest is aca.
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.util.InputMismatchException;
public class solution {
	public static long min(long a,long b)
	{
		if(a<b)
		{
			return a;
		}
		return b;
	}
	public static int isAvail(boolean[] avail,char c)
	{
		for(int i=c-96;i<26;i++)
		{
			if(avail[i])
				return i;
		}
		return -1;
	}
	public static void main(String args[]) throws Exception 
		{
			InputReader sc = new InputReader(System.in);
			PrintWriter out = new PrintWriter(System.out);
			int n = sc.nextInt();
			int k = sc.nextInt();
			String st = sc.readString();
			boolean[] avail = new boolean[26];
			StringBuffer ans = new StringBuffer(n);
			for(int i=0;i<n;i++)
			{
				avail[st.charAt(i)-97] = true;
			}
			if(k<=n)
			{
			for(int i=k-1;i>=0;i--)
			{
				int j = isAvail(avail,st.charAt(i)); 
				if(j!=-1)
				{
					ans.append(st.substring(0,i));
					ans.append((char)(j+97));
					break;
				}
			}
			}
			else
			{
				ans.append(st);
			}
			if(ans.length()<k)
			{
				int i = 0;
				for(;i<26;i++)
				{
					if(avail[i])
						break;
				}
				String c = ""+(char)(i+97);
				c = new String(new char[k-ans.length()]).replace("\0", c);
				ans.append(c);
			}
			out.println(ans);
			out.close();
		}
	static class InputReader {
		 
        private InputStream stream;
        private 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 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 int[] readCharCount() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            int[] map = new int[256];
            do {
                int val = c ;
                map[val]++;
                c = snext();
            } while (!isSpaceChar(c));
            return map;
        }
 
        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
 
}