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
#include <cstdio>
#include <algorithm>
using namespace std;

const int Maxn = 5000;

int N, K;
char s[Maxn * 2 + 5], ans[Maxn * 2 + 5];
char mn, mx;

void check(char *str, int k) {
	char t[Maxn * 2 + 5];
	int now = N, len = 0;
	while(now >= 1 && str[now] == mn)
		now--, len++;
	while(k != 0 && len < N)
		len *= 2, k--;
	if(len >= N) {
		for(int i = 1; i <= N; i++)
			ans[i] = mn;
		puts(ans + 1);
		exit(0);
	}
	for(int i = 1; i <= len; i++)
		t[i] = mn;
	for(int i = len + 1; i <= N; i++)
		t[i] = str[now--];
	for(int i = 1; i <= N; i++)
		if(t[i] < ans[i]) {
			for(int j = 1; j <= N; j++)
				ans[j] = t[j];
			return;
		} else if(t[i] > ans[i]) return;
}

int main() {
#ifdef LOACL
	freopen("in.txt", "r", stdin);
	freopen("out.txt", "w", stdout);
#endif
	scanf("%d %d %s", &N, &K, s + 1);
	mn = 'z', mx = 'a';
	for(int i = 1; i <= N; i++) {
		mn = min(mn, s[i]);
		mx = max(mx, s[i]);
		s[2 * N - i + 1] = s[i];
		ans[i] = 'z';
	}
	if(mn == mx) {
		puts(s + 1);
		return 0;
	}
	if(s[N] == mn)
		check(s, K);
	for(int i = N; i <= 2 * N; i++)
		if(s[i] == mn) check(s + i - N, K - 1);
	puts(ans + 1);
	return 0;
}