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.

//package codeTrainingLeetcode;

import java.util.Scanner;
import java.util.TreeSet;

public class C466D2C {
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		int sLen = scanner.nextInt();
		int tLen = scanner.nextInt();
		String string = scanner.next();
		char[] res = new char[tLen];
		TreeSet<Character> treeSet = new TreeSet<>();
		char minChar = (char) ('z' + 1);
		for (int i = 0; i < sLen; i++) {
			char tmp = string.charAt(i);
			treeSet.add(tmp);
			minChar = (char) Math.min(minChar, tmp);
		}
		if (tLen > sLen) {
			System.out.print(string);
			for (int i = 0; i < tLen - sLen; i++)
				System.out.print(minChar);
			System.out.println();
			return;
		}
		for (int i = tLen - 1; i >= 0; i--) {
			char tmp = string.charAt(i);
			Character nextChar = treeSet.higher(tmp);
			if (nextChar != null) {
				res[i] = nextChar;
				System.arraycopy(string.toCharArray(), 0, res, 0, i);
				System.out.println(String.valueOf(res));
				return;
			} else {
				res[i] = minChar;
			}
		}
		return;
	}
}
