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>
#define syosu(x) fixed<<setprecision(x)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> P;
typedef pair<double,double> pdd;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<string> vs;
typedef vector<P> vp;
typedef vector<vp> vvp;
typedef vector<pll> vpll;
typedef pair<int,P> pip;
typedef vector<pip> vip;
const int inf=1<<30;
const ll INF=1ll<<55;
const double pi=acos(-1);
const double eps=1e-8;
const ll mod=1e9+7;
const int dx[4]={-1,0,1,0},dy[4]={0,-1,0,1};

int n,k;
string s;

int main(){
	cin>>n>>k>>s;
	char c=(char)('z'+1);
	int m,I=0;
	string s_=s;
	reverse(s_.begin(),s_.end());
	s+=s_+'#';
	for(int i=1;i<=2*n;i++) if(s[i]!=s[i-1]){
		if(s[I]<c) c=s[I],m=i-I;
		else if(s[I]==c&&i-I>m) m=i-I;
		I=i;
	}
	string res;
	res+=(char)('z'+1);
	int M=min(n,(k>=14?n:m*(1<<(k-1))));
	for(int i=0;i<n;i++) if(s.substr(i,m)==string(m,c)){
		string t(M,c);
		for(int j=0;j<n-M;j++) t+=s[i+j+m];
		res=min(res,t);
	}
	cout<<res<<endl;
}
