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.
n,k = map(int, raw_input().split())
nap_in = str(raw_input())
tab = [0] * 26
tab_lit = []
wyn = ''
mini = 27
maxi = -1
for x in range(0, len(nap_in), +1):
    tab[ord(nap_in[x])-97] += 1
for x in range(0, len(tab), +1):
    if tab[x] != 0:
        tab_lit.append(x)
mini = tab_lit[0]
maxi = tab_lit[-1]
if k>n:
    wyn = nap_in
    for x in range(0, k-n, +1):
        wyn += chr(mini+97)
    print wyn
    exit(0)
for x in range(0, k, +1):
    wyn += nap_in[x]
y = k-1
z = 2
wyn_list = list(wyn)
while True:
    if wyn[y] == chr(maxi+97):
        wyn_list[y] = chr(mini+97)
        y -= 1
    else:
        for x in range(ord(wyn[y])-97+1, 26, +1):
            if tab[x] != 0:
                wyn_list[y] = chr(x+97)
                #print wyn_list
                print ''.join(wyn_list)
                exit(0)