Problem:
Score : 300 points

Problem Statement

You are given a string s.
Among the different substrings of s, print the K-th lexicographically smallest one.

A substring of s is a string obtained by taking out a non-empty contiguous part in s.
For example, if s = ababc, a, bab and ababc are substrings of s, while ac, z and an empty string are not.
Also, we say that substrings are different when they are different as strings.

Let X = x_{1}x_{2}...x_{n} and Y = y_{1}y_{2}...y_{m} be two distinct strings. X is lexicographically larger than Y if and only if Y is a prefix of X or x_{j} > y_{j} where j is the smallest integer such that x_{j} \neq y_{j}.

Constraints

1 ≤ |s| ≤ 5000

s consists of lowercase English letters.

1 ≤ K ≤ 5

s has at least K different substrings.

Partial Score

200 points will be awarded as a partial score for passing the test set satisfying |s| ≤ 50.

Input

Input is given from Standard Input in the following format:

s
K

Output

Print the K-th lexicographically smallest substring of K.

Sample Input 1

aba
4

Sample Output 1

b

s has five substrings: a, b, ab, ba and aba.
Among them, we should print the fourth smallest one, b.
Note that we do not count a twice.

Sample Input 2

atcoderandatcodeer
5

Sample Output 2

andat

Sample Input 3

z
1

Sample Output 3

z

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.IOException;
import java.io.InputStream;
import java.util.HashSet;
import java.util.NoSuchElementException;
import java.util.Set;
import java.util.TreeSet;

public class Main {
	public static void main(String[] args) {
		FastScanner sc = new FastScanner();
		String s = sc.next();
		int K = sc.nextInt();
		Set<String> set = new HashSet<String>();
		int len = s.length();
		for (int i = 0; i < len; i++) {
			for (int j = i + 1; j <= len; j++) {
				String sub = s.substring(i, j);
				set.add(sub);
			}
		}
		int count = 1;
		String ans = "";
		set = new TreeSet<String>(set);
		for (String t : set) {
			if (count == K) {
				ans = t;
				break;
			}
			count++;
		}
		out(ans);
	}



	static class Combination {
		final int mod;
		final int max;

		final long[] fact;
		final long[] inv;
		final long[] invfact;

		public Combination(int n) {
			this(n, 1_000_000_007);
		}

		public Combination(int n, int mod) {
			this.mod = mod;
			max = n + 1;
			fact = new long[max];
			invfact = new long[max];
			inv = new long[max];

			inv[1] = 1;
			for (int i = 2; i < inv.length; i++) {
				inv[i] = inv[mod % i] * (mod - mod / i) % mod;
			}

			fact[0] = 1;
			invfact[0] = 1;
			for (int i = 1; i < inv.length; i++) {
				fact[i] = i * fact[i - 1] % mod;
				invfact[i] = inv[i] * invfact[i - 1] % mod;
			}
		}

		public long get(int n, int r) {
			return fact[n] * invfact[n - r] % mod * invfact[r] % mod;
		}
	}


	public static long gcd(long a, long b) {
		long remainder = a % b;
		if (remainder == 0) {
			return b;
		} else {
			return gcd(b, remainder);
		}
	}

	static void out(String a) {
		System.out.println(a);
	}

	static void out(int a) {
		System.out.println(a);
	}

	static void out(long a) {
		System.out.println(a);
	}

	static void out(double a) {
		System.out.println(a);
	}

	static void out(char a) {
		System.out.println(a);
	}
}


class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        } else {
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }

    private int readByte() {
        if (hasNextByte())
            return buffer[ptr++];
        else
            return -1;
    }

    private static boolean isPrintableChar(int c) {
        return 33 <= c && c <= 126;
    }

    public boolean hasNext() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr]))
            ptr++;
        return hasNextByte();
    }

    public String next() {
        if (!hasNext())
            throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    public long nextLong() {
        if (!hasNext())
            throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while (true) {
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            } else if (b == -1 || !isPrintableChar(b)) {
                return minus ? -n : n;
            } else {
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }

    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
            throw new NumberFormatException();
        return (int) nl;
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }
}