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 (1.14.1) (judge verdict: Accepted)

package main

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

var (
	finv, inv, fac [MAX]int
)

func COM(n, k int) int {
	MOD := int(MOD)
	if n < k {
		return 0
	}
	if n < 0 || k < 0 {
		return 0
	}
	return fac[n] * (finv[k] * finv[n-k] % MOD) % MOD
}

func init() {
	MOD := int(MOD)
	fac[0] = 1
	fac[1] = 1
	finv[0] = 1
	finv[1] = 1
	inv[1] = 1
	for i := 2; i < MAX; i++ {
		fac[i] = fac[i-1] * i % MOD
		inv[i] = MOD - inv[MOD%i]*(MOD/i)%MOD
		finv[i] = finv[i-1] * inv[i] % MOD
	}
	//sc.Split(bufio.ScanLines)
	sc.Split(bufio.ScanWords)
	sc.Buffer([]byte{}, 500100)
}

const (
	MAX = 510000
)

var MOD int64 = 1000000007

func ModAdd(a, b int64) int64 {
	return (a + b) % MOD
}

func ModMul(a, b int64) int64 {
	ans := a * b % MOD
	if ans < 0 {
		ans += MOD
	}
	return ans
}

func ModSub(a, b int64) int64 {
	r := (a%MOD - b%MOD) % MOD
	if r < 0 {
		r += MOD
	}
	return r
}

func ModDiv(a, b int64) int64 {
	return a % MOD * ModInv(b) % MOD
}

func ModPow(a, n int64) int64 {
	var r int64 = 1
	for n > 0 {
		if n&1 == 1 {
			r = r * a % MOD
		}
		a = a * a % MOD
		n >>= 1
	}
	return r
}

func ModInv(a int64) int64 {
	var b, u, v int64 = MOD, 1, 0
	for b > 0 {
		t := a / b
		a -= t * b
		a, b = b, a
		u -= t * v
		u, v = v, u
	}
	u %= MOD
	if u < 0 {
		u += MOD
	}
	return u
}

type Q struct {
	value int
	index int
	K     int
}

type QS []*Q

func (p QS) Len() int           { return len(p) }
func (p QS) Less(i, j int) bool { return p[i].value > p[j].value }
func (pq QS) Swap(i, j int) {
	pq[i], pq[j] = pq[j], pq[i]
	pq[i].index = i
	pq[j].index = j
}

func (pq *QS) Push(x interface{}) {
	n := len(*pq)
	item := x.(*Q)
	item.index = n
	*pq = append(*pq, item)
}

func (pq *QS) Pop() interface{} {
	old := *pq
	n := len(old)
	item := old[n-1]
	old[n-1] = nil  // avoid memory leak
	item.index = -1 // for safety
	*pq = old[0 : n-1]
	return item
}

func GCD(a, b int64) int64 {
	if b == 0 {
		return a
	}
	return GCD(b, a%b)
}

func LCM(a, b int64) int64 {
	return a * b / GCD(a, b)
}

type UnionFind struct {
	par  []int
	size []int
}

func NewUnionFind(size int) *UnionFind {
	return new(UnionFind).init(size)
}

func (uf *UnionFind) init(size int) *UnionFind {
	uf.par = make([]int, size)
	uf.size = make([]int, size)

	for i := 0; i < size; i++ {
		uf.par[i] = i
		uf.size[i] = 1
	}
	return uf
}

func (uf *UnionFind) Unite(p int, q int) {
	rp := uf.Root(p)
	rq := uf.Root(q)
	if rp == rq {
		return
	}
	if uf.size[rp] < uf.size[rq] {
		uf.par[rp] = uf.par[rq]
		uf.size[rq] += uf.size[rp]
	} else {
		uf.par[rq] = uf.par[rp]
		uf.size[rp] += uf.size[rq]
	}
}

func (uf *UnionFind) Root(p int) int {
	for uf.par[p] == p {
		return p
	}
	uf.par[p] = uf.Root(uf.par[p])
	return uf.par[p]
}

func (uf *UnionFind) Size(p int) int {
	return uf.size[uf.Root(p)]
}

func (uf *UnionFind) Same(p int, q int) bool {
	return uf.Root(p) == uf.Root(q)
}

var sc = bufio.NewScanner(os.Stdin)

func getInt() int {
	n, _ := strconv.Atoi(getStr())
	return n
}

func getStr() string {
	sc.Scan()
	return sc.Text()
}

func factor(result map[int]int, num, pnum int) map[int]int {
	if pnum*pnum > num {
		if num != 1 {
			result[num] += 1
		}
		return result
	}

	if num%pnum == 0 {
		num /= pnum
		result[pnum]++
	} else {
		pnum++
	}
	return factor(result, num, pnum)
}

func main() {
	N := []rune(getStr())
	K := getInt()
	m := map[string]bool{}
	ans := make([]string, 0, 5000*5000)
	for i := 0; i < len(N); i++ {
		for j := i + 1; j <= i+1+K; j++ {
			if j > len(N) {
				continue
			}
			s := string(N[i:j])
			if m[s] {
				continue
			}
			m[s] = true
			ans = append(ans, s)
		}
	}
	sort.Strings(ans)
	//fmt.Println(K, ans, len(N), len(ans), len(N)*(len(N)-1))
	fmt.Println(ans[K-1])
}

type IntHeap []int

func (h IntHeap) Len() int           { return len(h) }
func (h IntHeap) Less(i, j int) bool { return h[i] > h[j] }
func (h IntHeap) Swap(i, j int)      { h[i], h[j] = h[j], h[i] }

func (h *IntHeap) Push(x interface{}) {
	// Push and Pop use pointer receivers because they modify the slice's length,
	// not just its contents.
	*h = append(*h, x.(int))
}

func (h *IntHeap) Pop() interface{} {
	old := *h
	n := len(old)
	x := old[n-1]
	*h = old[0 : n-1]
	return x
}

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