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.util.*;
import java.io.*;

public class C940 {
	static BufferedReader in;
	static StringTokenizer st;
	static PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
	
	public static void main(String[] args) throws Exception {

		st = new StringTokenizer(in.readLine());
		int n = i(), len = i();

		char[] s = in.readLine().toCharArray();

		TreeSet<Character> t = new TreeSet<>();

		for (char c : s) {
			t.add(c);
		}

		if (len > n) {
			for (char c : s) {
				out.print(c);
			}
			for (int i = len - n; i > 0; i--) {
				out.print(t.first());
			}
			out.println();
		} else {
			for (int i = len - 1; i >= 0; i--) {
				Character c = t.higher(s[i]);
				if (c != null) {
					s[i] = c;
					break;
				} else {
					s[i] = t.first();
				}
			}
			for (int i = 0; i < len; i++) {
				out.print(s[i]);
			}
			out.println();
		}

		out.close();
	}

	static {
		try {
			in = new BufferedReader(new FileReader("cf.in"));
		} catch (Exception e) {
			in = new BufferedReader(new InputStreamReader(System.in));
		}
	}
	static int i() {return Integer.parseInt(st.nextToken());}
	static double d() {return Double.parseDouble(st.nextToken());}
	static String s() {return st.nextToken();}
	static long l() {return Long.parseLong(st.nextToken());}
}
