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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"sort"
)

func main() {
	r := bufio.NewReader(os.Stdin)
	var s string
	var k int
	fmt.Fscan(r, &s)
	fmt.Fscan(r, &k)

	mp := make(map[string]bool)
	var ss []string
	for i := 1; i <= k; i++ {
		for j := 0; i+j <= len(s); j++ {
			tmpS := s[j : i+j]
			if mp[tmpS] == false {
				ss = append(ss, tmpS)
				mp[tmpS] = true
			}
		}
	}

	sort.Strings(ss)

	fmt.Println(ss[k-1])
}

// Union-Find
type unionFind struct {
	d []int
}

func newUnionFind(n int) *unionFind {
	uf := new(unionFind)
	uf.d = make([]int, n)
	for i := 0; i < n; i++ {
		uf.d[i] = -1
	}
	return uf
}

func (uf *unionFind) find(x int) int {
	if uf.d[x] < 0 {
		return x
	}
	uf.d[x] = uf.find(uf.d[x])
	return uf.d[x]
}

func (uf *unionFind) unite(x, y int) bool {
	rootX := uf.find(x)
	rootY := uf.find(y)
	if rootX == rootY {
		return false
	}

	if uf.d[rootX] < uf.d[rootY] {
		uf.d[rootX] += uf.d[rootY]
		uf.d[rootY] = rootX
	} else {
		uf.d[rootY] += uf.d[rootX]
		uf.d[rootX] = rootY
	}

	return true
}

func (uf *unionFind) same(x, y int) bool {
	return uf.find(x) == uf.find(y)
}

func (uf *unionFind) size(x int) int {
	return -uf.d[uf.find(x)]
}

// mod combination
func modpow(a, n, mod int) int {
	res := 1
	for n > 0 {
		if n%2 != 0 {
			res = res * a % mod
		}
		a = a * a % mod
		n = n / 2
	}
	return res
}

func modcomb(n, a, mod int) int {
	x := 1
	y := 1
	for i := 0; i < a; i++ {
		x = x * (n - i)
		x %= mod
		y = y * (i + 1)
		y %= mod
	}
	return x * modpow(y, mod-2, mod) % mod
}

func modfactorial(n, mod int) int {
	result := 1
	for i := 1; i <= n; i++ {
		result = (result * i) % mod
	}
	return result
}

// Utility

func min(x, y int) int {
	if x < y {
		return x
	}
	return y
}

func max(x, y int) int {
	if x > y {
		return x
	}
	return y
}

func abs(x int) int {
	if x < 0 {
		return -x
	}
	return x
}

func primeFactor(x int) map[int]int {
	res := make(map[int]int)
	for i := 2; i*i <= x; i++ {
		for x%i == 0 {
			res[i]++
			x = x / i
		}
	}
	if x != 1 {
		res[x] = 1
	}
	return res
}

func divisor(x int) []int {
	res := make([]int, 0)
	for i := 1; i*i <= x; i++ {
		if x%i == 0 {
			res = append(res, i)
			if i != x/i {
				res = append(res, x/i)
			}
		}
	}
	return res
}

func gcd(x, y int) int {
	if y == 0 {
		return x
	}
	return gcd(y, x%y)
}

func lcm(x, y int) int {
	return x / gcd(x, y) * y
}

func reverseString(s string) string {
	r := []rune(s)
	for i, j := 0, len(r)-1; i < len(r)/2; i, j = i+1, j-1 {
		r[i], r[j] = r[j], r[i]
	}
	return string(r)
}

// Queue ...
type Queue []int

// pop ...
func (q *Queue) empty() bool {
	return len(*q) == 0
}

// push ...
func (q *Queue) push(i int) {
	*q = append(*q, i)
}

// pop ...
func (q *Queue) pop() (int, bool) {
	if q.empty() {
		return 0, false
	} else {
		res := (*q)[0]
		*q = (*q)[1:]
		return res, true
	}
}

// Stack ...
type Stack []int

// pop ...
func (s *Stack) empty() bool {
	return len(*s) == 0
}

// push ...
func (s *Stack) push(i int) {
	*s = append(*s, i)
}

// pop ...
func (s *Stack) pop() (int, bool) {
	if s.empty() {
		return 0, false
	} else {
		index := len(*s) - 1
		res := (*s)[index]
		*s = (*s)[:index]
		return res, true
	}
}