Problem: You are given a string t consisting of n lowercase Latin letters and an integer number k.

Let's define a substring of some string s with indices from l to r as s[l ... r].

Your task is to construct such string s of minimum possible length that there are exactly k positions i such that s[i ... i + n - 1] = t. In other words, your task is to construct such string s of minimum possible length that there are exactly k substrings of s equal to t.

It is guaranteed that the answer is always unique.

Input

The first line of the input contains two integers n and k (1 ≤ n, k ≤ 50) — the length of the string t and the number of substrings.

The second line of the input contains the string t consisting of exactly n lowercase Latin letters.

Output

Print such string s of minimum possible length that there are exactly k substrings of s equal to t.

It is guaranteed that the answer is always unique.

Examples

Input

3 4
aba


Output

ababababa


Input

3 2
cat


Output

catcat

Solution (in JAVA):

Solution:
/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

/**
 *
 * @author dipankar12
 */
import java.io.*;
import java.util.*;
public class r506a {
    public static void main(String args[])
    {
        fastio in=new fastio(System.in);
        PrintWriter pw=new PrintWriter(System.out);

        int n=in.nextInt();
        int k=in.nextInt();
        
        String str=in.readString();
        int count=0;
        for(int i=1;i<n;i++)
        {
            boolean yes=true;
            int x=0;
            for(int j=i;j<n;j++)
            {
                if(str.charAt(j)==str.charAt(x))
                    x++;
                else
                {
                    yes=false;
                    break;
                }
            }
            
            if(yes)
                count=Math.max(count, n-i);
        }
        int rem=n-count;
        
        String ans=str;
        //pw.println(rem+" "+str.substring(n-rem,n));
        for(int i=0;i<k-1;i++)
            ans+=str.substring(n-rem,n);
        
        pw.println(ans);
        pw.close();
    }

    static class fastio {
     
            private final InputStream stream;
            private final byte[] buf = new byte[8192];
            private int cchar, snchar;
            private SpaceCharFilter filter;
     
            public fastio(InputStream stream) {
                this.stream = stream;
            }
     
            public int nxt() {
                if (snchar == -1)
                    throw new InputMismatchException();
                if (cchar >= snchar) {
                    cchar = 0;
                    try {
                        snchar = stream.read(buf);
                    } catch (IOException e) {
                        throw new InputMismatchException();
                    }
                    if (snchar <= 0)
                        return -1;
                }
                return buf[cchar++];
            }
     
            public int nextInt() {
                int c = nxt();
                while (isSpaceChar(c)) {
                    c = nxt();
                }
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = nxt();
                }
                int res = 0;
                do {
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = nxt();
                } while (!isSpaceChar(c));
                return res * sgn;
            }
     
            public long nextLong() {
                int c = nxt();
                while (isSpaceChar(c)) {
                    c = nxt();
                }
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = nxt();
                }
                long res = 0;
                do {
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = nxt();
                } while (!isSpaceChar(c));
                return res * sgn;
            }
     
            public int[] nextIntArray(int n) {
                int a[] = new int[n];
                for (int i = 0; i < n; i++) {
                    a[i] = nextInt();
                }
                return a;
            }
     
            public String readString() {
                int c = nxt();
                while (isSpaceChar(c)) {
                    c = nxt();
                }
                StringBuilder res = new StringBuilder();
                do {
                    res.appendCodePoint(c);
                    c = nxt();
                } while (!isSpaceChar(c));
                return res.toString();
            }
     
            public String nextLine() {
                int c = nxt();
                while (isSpaceChar(c))
                    c = nxt();
                StringBuilder res = new StringBuilder();
                do {
                    res.appendCodePoint(c);
                    c = nxt();
                } while (!isEndOfLine(c));
                return res.toString();
            }
     
            public boolean isSpaceChar(int c) {
                if (filter != null)
                    return filter.isSpaceChar(c);
                return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
            }
     
            private boolean isEndOfLine(int c) {
                return c == '\n' || c == '\r' || c == -1;
            }
     
            public interface SpaceCharFilter {
                public boolean isSpaceChar(int ch);
            }
        }
    

}