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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class Main {
	private static String s;
	private static int N, T;
	private static TreeSet<Integer> set = new TreeSet<Integer>();
	private static int[] str;
	private static int[] results;

	public static void main(String[] args) throws IOException {
		BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(f.readLine());
		N = Integer.parseInt(st.nextToken());
		T = Integer.parseInt(st.nextToken());
		s = f.readLine();
		results = new int[T];
		str = new int[N];
		for (int i = 0; i < N; i++) {
			int value = s.charAt(i) - 'a';
			set.add(value);
			str[i] = value;
		}
		if (T > N) {
			for (int i = 0; i < N; i++) {
				results[i] = str[i];
			}
			for (int i = N; i < T; i++) {
				results[i] = set.first();
			}
			System.out.println(print());
		} else {
			int index = T - 1;
			while (index >= 0) {
				if (str[index] != set.last()) {
					results[index] = set.ceiling(str[index] + 1);
					break;
				}
				results[index] = set.first();
				index--;
			}
			for (int i = index - 1; i >= 0; i--) {
				results[i] = str[i];
			}
			System.out.println(print());
		}
	}

	public static String print() {
		StringBuilder sb = new StringBuilder();
		for (int i : results) {
			sb.append((char) ('a' + i));
		}
		return sb.toString();
	}
}