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.HashSet;
import java.util.Scanner;


public class PhoneNumbers {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub

		Scanner input = new Scanner(System.in);
		int n = input.nextInt();
		int k  = input.nextInt();
		char[] s = input.next().toCharArray();
		char[] p = new char[k];
		HashSet<Character> set = new HashSet<Character>();
		for(int i=0; i<s.length;i++){
			set.add(s[i]);
		}
		char min='z'+1;
		for(char c : set){
			if(c<min)min =c;
		}
		if(n<k){
			System.out.print(s);
			for(int i=0; i<k-n;i++)System.out.print(min);
			return;
			
		}
		
		int i=Math.min(k-1,n-1);
		while(i>=0){
			if(contains(set,s[i])!='0'){
				p[i] = contains(set,s[i]);
				//System.out.println(i);
				for(int j=i-1; j>=0;j--){
					p[j] = s[j];
				}
				for(int j=i+1; j<k;j++){
					 p[j] = min;
				}
				for(int j=0; j<k;j++)System.out.print(p[j]);
				return;
			}
			
			
			
			i--;
		}
	}
	
	private static char contains(HashSet<Character> set, char p){
		
		char min  = 'z'+1;
		for(char c : set){
			if(c>p && c<min){
				min = c;
			}
		}
		if(min !=('z'+1)){
			return min;
		}
		else
			return '0';
	}

}
