Takahashi has a string S of length N consisting of lowercase English letters. On this string, he will perform the following operation K times:

* Let T be the string obtained by reversing S, and U be the string obtained by concatenating S and T in this order.
* Let S' be some contiguous substring of U with length N, and replace S with S'.



Among the strings that can be the string S after the K operations, find the lexicographically smallest possible one.

Constraints

* 1 \leq N \leq 5000
* 1 \leq K \leq 10^9
* |S|=N
* S consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:


N K
S


Output

Print the lexicographically smallest possible string that can be the string S after the K operations.

Examples

Input

5 1
bacba


Output

aabca


Input

10 2
bbaabbbaab


Output

aaaabbaabb
n, k = map(int, input().split())
s = input()
m = min(s)
for p in range(k):
    u = s + s[::-1]
    l = []
    cnt = 0
    idx = 0
    for i in range(n * 2):
        if u[i] == m:
            if cnt == 0:
                idx = i
            cnt += 1
        else:
            if cnt > 0:
                l.append((cnt, idx))
                cnt = 0
    if cnt > 0:
        l.append((cnt, idx))
    a, j = max(l)
    if a >= n:
        print(m * n)
        exit(0)
    for c, i in l:
        if i <= n and c == a:
            s = min(s, u[i:i + n])
    s = s[::-1]
print(s[::-1])
