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.awt.List;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.PrintWriter;
import java.lang.Math.*;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.Scanner;

public class Class_4 {
	public static int f(int time_in_1, int i, int n) {
		int time = (time_in_1 + i - 1) % n;
		if (time == 0) {
			return n;
		} else {
			return time;
		}
	}

	public static void main(String[] args) throws FileNotFoundException {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int k = in.nextInt();
		String s = in.next();
		char[] a = s.toCharArray();
		int []ex = new int[27];
		StringBuffer sub = new StringBuffer("");
		char min_abs = '}';
		Arrays.fill(ex, 0);
		for (int i = 0; i < n; ++i) {
			if (a[i] < min_abs) {
				min_abs = a[i];
			}
			int index = a[i] - 'a';
			if(ex[index] == 0)
			{
				ex[index] = 1;
			}
		}
		
		if (n >= k) {
			boolean tr = true;
			int min_index = k;
			char max = '}';
			while (tr) {
				tr = false;
				min_index--;
				char min = a[min_index];
				max = '}';
				for (int i = a[min_index] - 'a' + 1; i < 27; ++i) {
					if (ex[i] != 0) {
						max = (char)(i + 'a');
						break;
					}
				}
				if (max == '}') {
					tr = true;
				}
			}
			for (int i = 0; i < min_index; ++i) {
				sub.append(a[i]);
			}
			sub.append(max);
			for (int i = 0; i < k - min_index - 1; ++i) {
				sub.append(min_abs);
			}
			System.out.println(sub);

		} else {
			sub.append(s);
			for (int i = 0; i < k - n; ++i) {
				sub.append(min_abs);
			}
			System.out.println(sub);
		}

	}
}