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<bits/stdc++.h>
using namespace std;

int n, k;

string ans, a;

string solve (string &S) {
	if(k == 1) return S;
	char L = S.back();
	int C = 0;
	while(S.back() == L) {
		S.pop_back();
		C++;
	}
	C = min(n, C*(1<<min(k-1, 13)));
	string R;
	while(C--) R.push_back(L);
	while(R.size() < n) {
		R.push_back(S.back());
		S.pop_back();
	}
	return R;
}

int main()
{
	ans.push_back('z'+1);
	cin >> n >> k >> a;
	string b = a;
	reverse(b.begin(), b.end());
	a += b;
	for(int i=0;i<=n;i++) {
		string T = a.substr(i, n);
		ans = min(ans, solve(T));
	}
	cout << ans << endl;
}
