Problem:
Score: 400 points

Problem Statement

The Patisserie AtCoder sells cakes with number-shaped candles.
There are X, Y and Z kinds of cakes with 1-shaped, 2-shaped and 3-shaped candles, respectively.
Each cake has an integer value called deliciousness, as follows:

The deliciousness of the cakes with 1-shaped candles are A_1, A_2, ..., A_X.

The deliciousness of the cakes with 2-shaped candles are B_1, B_2, ..., B_Y.

The deliciousness of the cakes with 3-shaped candles are C_1, C_2, ..., C_Z.

Takahashi decides to buy three cakes, one for each of the three shapes of the candles, to celebrate ABC 123.

There are X \times Y \times Z such ways to choose three cakes.

We will arrange these X \times Y \times Z ways in descending order of the sum of the deliciousness of the cakes.

Print the sums of the deliciousness of the cakes for the first, second, ..., K-th ways in this list.

Constraints

1 \leq X \leq 1 \ 000

1 \leq Y \leq 1 \ 000

1 \leq Z \leq 1 \ 000

1 \leq K \leq \min(3 \ 000, X \times Y \times Z)

1 \leq A_i \leq 10 \ 000 \ 000 \ 000

1 \leq B_i \leq 10 \ 000 \ 000 \ 000

1 \leq C_i \leq 10 \ 000 \ 000 \ 000

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X Y Z K
A_1 \ A_2 \ A_3 \ ... \ A_X
B_1 \ B_2 \ B_3 \ ... \ B_Y
C_1 \ C_2 \ C_3 \ ... \ C_Z

Output

Print K lines. The i-th line should contain the i-th value stated in the problem statement.

Sample Input 1

2 2 2 8
4 6
1 5
3 8

Sample Output 1

19
17
15
14
13
12
10
8

There are 2 \times 2 \times 2 = 8 ways to choose three cakes, as shown below in descending order of the sum of the deliciousness of the cakes:

(A_2, B_2, C_2): 6 + 5 + 8 = 19

(A_1, B_2, C_2): 4 + 5 + 8 = 17

(A_2, B_1, C_2): 6 + 1 + 8 = 15

(A_2, B_2, C_1): 6 + 5 + 3 = 14

(A_1, B_1, C_2): 4 + 1 + 8 = 13

(A_1, B_2, C_1): 4 + 5 + 3 = 12

(A_2, B_1, C_1): 6 + 1 + 3 = 10

(A_1, B_1, C_1): 4 + 1 + 3 = 8

Sample Input 2

3 3 3 5
1 10 100
2 20 200
1 10 100

Sample Output 2

400
310
310
301
301

There may be multiple combinations of cakes with the same sum of the deliciousness. For example, in this test case, the sum of A_1, B_3, C_3 and the sum of A_3, B_3, C_1 are both 301.
However, they are different ways of choosing cakes, so 301 occurs twice in the output.

Sample Input 3

10 10 10 20
7467038376 5724769290 292794712 2843504496 3381970101 8402252870 249131806 6310293640 6690322794 6082257488
1873977926 2576529623 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338
4975681328 8974383988 2882263257 7690203955 514305523 6679823484 4263279310 585966808 3752282379 620585736

Sample Output 3

23379871545
22444657051
22302177772
22095691512
21667941469
21366963278
21287912315
21279176669
21160477018
21085311041
21059876163
21017997739
20703329561
20702387965
20590247696
20383761436
20343962175
20254073196
20210218542
20150096547

Note that the input or output may not fit into a 32-bit integer type.

Solution in Go (1.6) (judge verdict: Runtime Error)

package main

import (
	"bufio"
	"fmt"
	"io"
	"math"
	"os"
	"sort"
	"strconv"
	"strings"

)


func main() {
	solve(os.Stdin, os.Stdout)
}

type ReaderEx struct {
	baseScanner *bufio.Scanner
	words       []string
	nextWordIdx func() int
	initWordIdx func(int)
}

func NewScannerEx(stdin io.Reader) *ReaderEx {
	var this ReaderEx
	var idx int
	var wordsCnt int
	this.baseScanner = bufio.NewScanner(stdin)
	this.baseScanner.Buffer(make([]byte, 0), 1E+11)
	this.nextWordIdx = func() int {
		cur := idx
		idx = (idx + 1) % wordsCnt
		return cur
	}
	this.initWordIdx = func(wc int) {
		idx = 0
		wordsCnt = wc
	}
	return &this
}

func (me *ReaderEx) Scan(doSplit bool) (isScanned bool) {
	isScanned = me.baseScanner.Scan()
	if doSplit {
		me.words = strings.Fields(me.baseScanner.Text())
	} else {
		me.words = []string{me.baseScanner.Text()}
	}
	me.initWordIdx(len(me.words))
	return
}

func (me *ReaderEx) nextBytes() []byte {
	return []byte(me.words[me.nextWordIdx()])
}
func (me *ReaderEx) nextString() string {
	return me.words[me.nextWordIdx()]
}

type StringArray []string

func (me *ReaderEx) nextStringArray() StringArray {
	return me.words[me.nextWordIdx():]
}

func (me StringArray) toStrings() []string {
	return me
}

func (me StringArray) toInts() []int {
	strValues := me.toStrings()
	values := make([]int, len(strValues))
	for i, v := range strValues {
		n, err := strconv.Atoi(v)
		if err != nil {
			panic(err)
		}
		values[i] = n
	}
	return values
}
func (me *ReaderEx) nextInt() int {
	n, err := strconv.Atoi(me.words[me.nextWordIdx()])

	defer func() {
		if err != nil {
			panic(fmt.Sprintf("getInt(%d)", n))
		}
	}()
	return n
}

func pow(x, y, mod int) (ans int) {

	ans = 1
	for bit := 1 << uint(math.Floor(math.Log2(float64(y)))); ; bit >>= 1 {
		if y&bit != 0 {
			ans *= x
			if mod > 0 {
				ans %= mod
			}
		}
		if bit <= 1 {
			return
		}
		ans *= ans
		if mod > 0 {
			ans %= mod
		}
	}
}

type factType struct {
	prime int
	count int
}

func fact(n int) (facts []*factType) {

	for i := 2; i*i <= n; i++ {
		if n%i == 0 {
			fa := factType{prime: i}
			for n%fa.prime == 0 {
				n /= fa.prime
				fa.count++
			}
			facts = append(facts, &fa)
		}
	}
	if n > 1 {
		facts = append(facts, &factType{prime: n, count: 1})
	}
	return facts
}
func dec2bin(n int) (ret []bool) {
	for bit := 1 << uint(math.Floor(math.Log2(float64(n)))); ; bit >>= 1 {
		ret = append(ret, n&bit != 0)

		if bit <= 1 {
			return
		}
	}

}

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

func b2i(b bool) (i int) {
	if b {
		i = 1
	} else {
		i = 0
	}
	return
}

//RBNodeDir is
type RBNodeDir int

const (

	//RBNodeLeft 左方向
	RBNodeLeft RBNodeDir = iota

	//RBNodeRight 右方向
	RBNodeRight

	//RBNodeHere ここ
	RBNodeHere
)

//RBNode is
type RBNode struct {
	isRed    bool
	index    int
	parent   *RBNode
	children [2]*RBNode
}

//RBCursor is
type RBCursor struct {
	node *RBNode
	less func(i int, j int) bool
}

func (cur *RBCursor) clone() *RBCursor {
	wrk := *cur
	return &wrk
}

func (cur *RBCursor) root() *RBCursor {

	if cur.node != nil {
		for ; cur.node.parent != nil; cur.node = cur.node.parent {

		}
	}
	return cur
}

func (cur *RBCursor) move(dir RBNodeDir) *RBCursor {
	if cur.node == nil {
		return cur
	}
	rev := dir ^ 1
	if next := cur.node.children[dir]; next != nil {
		for next.children[rev] != nil {
			next = next.children[rev]
		}
		cur.node = next
	} else {
		find := false
		for cur.node.parent != nil {
			now := cur.node
			cur.node = cur.node.parent
			if cur.node.children[rev] == now {
				find = true
				break
			}
		}
		if !find {
			cur.node = nil
		}
	}
	return cur
}
func (cur *RBCursor) find(index int) (*RBCursor, RBNodeDir) {
	cur.root()
	dir := RBNodeHere
	for {
		if cur.less(index, cur.node.index) {
			dir = RBNodeLeft
			next := cur.node.children[dir]
			if next == nil {
				break
			}
			cur.node = next

		} else if cur.less(cur.node.index, index) {
			dir = RBNodeRight
			next := cur.node.children[dir]
			if next == nil {
				break
			}
			cur.node = next
		} else {
			dir = RBNodeHere
			break
		}
	}
	return cur, dir
}

func (cur *RBCursor) add(index int) *RBCursor {
	newNode := &RBNode{index: index, isRed: true}
	cur.root()
	if cur.node != nil {
		pnode, dir := cur.find(newNode.index)
		if dir != RBNodeHere {
			newNode.parent = pnode.node
			newNode.parent.children[dir] = newNode

			wrk := cur.clone()
			wrk.node = newNode
			wrk.opt()
		} else {
			pnode.node.index = newNode.index
			newNode = pnode.node
		}
	}
	cur.node = newNode
	return cur
}

func (node *RBNode) sibiling(child *RBNode) *RBNode {
	dir := RBNodeLeft
	if node.children[RBNodeLeft] == child {
		dir = RBNodeRight
	}
	return node.children[dir]
}

func (node *RBNode) flip(dir RBNodeDir) {
	curGranPa := node.parent
	newParent := node.children[dir]
	newParent.parent, node.parent = node.parent, newParent

	node.children[dir] = newParent.children[dir^1]
	if node.children[dir] != nil {
		node.children[dir].parent = node
	}
	newParent.children[dir^1] = node

	if curGranPa != nil {
		dir = RBNodeLeft
		if curGranPa.children[dir] != node {
			dir ^= 1
		}
		curGranPa.children[dir] = newParent
	}

}
func (cur *RBCursor) opt() {
	node := cur.node
	for node != nil && node.isRed {
		parent := node.parent
		if parent == nil {
			break
		} else if !parent.isRed {
			break
		} else if parent.parent == nil {
			parent.isRed = false
		} else {
			grandparent := parent.parent
			parentsibiling := grandparent.sibiling(parent)
			if parentsibiling != nil && parentsibiling.isRed {
				grandparent.isRed = true
				parent.isRed = false
				parentsibiling.isRed = false
				node = grandparent
			} else {
				dir := RBNodeLeft
				if grandparent.children[dir] != parent {
					dir ^= 1
				}

				if parent.children[dir] != node {
					parent.flip(dir ^ 1)
				}

				grandparent.flip(dir)
				grandparent.parent.isRed = false
				grandparent.isRed = true
				break
			}
		}
	}
}

func (cur *RBCursor) end(dir RBNodeDir) *RBCursor {
	cur.root()
	if cur.node != nil {
		for ; cur.node.children[dir] != nil; cur.node = cur.node.children[dir] {

		}
	}
	return cur
}

func solve(stdin io.Reader, stdout io.Writer) {

	r := NewScannerEx(stdin)
	r.Scan(true)
	x, y, z, k := r.nextInt(), r.nextInt(), r.nextInt(), r.nextInt()
	r.Scan(true)
	a := r.nextStringArray().toInts()
	r.Scan(true)
	b := r.nextStringArray().toInts()
	r.Scan(true)
	c := r.nextStringArray().toInts()

	type cursor struct {
		s          int
		ai, bi, ci int
		cnt        int
	}
	s := make([]*cursor, 0, k*3)
	tree := RBCursor{less: func(a, b int) bool {
		switch {
		case s[a].s != s[b].s:
			return s[a].s > s[b].s
		case s[a].ai != s[b].ai:
			return s[a].ai > s[b].ai
		case s[a].bi != s[b].bi:
			return s[a].bi > s[b].bi
		default:
			return s[a].ci > s[a].ci
		}
	}}
	sAdd := func(pp *cursor) {
		pp.s = a[pp.ai] + b[pp.bi] + c[pp.ci]
		pp.cnt = 1
		s = append(s, pp)
		tree.add(len(s) - 1)
	}
	sort.Sort(sort.Reverse(sort.IntSlice(a)))
	sort.Sort(sort.Reverse(sort.IntSlice(b)))
	sort.Sort(sort.Reverse(sort.IntSlice(c)))
	sAdd(&cursor{ai: 0, bi: 0, ci: 0})
	cur := tree.clone()

	for i := 0; i < k; i++ {
		pp := s[cur.node.index]
		fmt.Fprintln(stdout, pp.s)
		if pp.ai+1 < x {
			sAdd(&cursor{ai: pp.ai + 1, bi: pp.bi, ci: pp.ci})
		}
		if pp.bi+1 < y {
			sAdd(&cursor{ai: pp.ai, bi: pp.bi + 1, ci: pp.ci})
		}
		if pp.ci+1 < z {
			sAdd(&cursor{ai: pp.ai, bi: pp.bi, ci: pp.ci + 1})
		}
		cur, _ = cur.find(cur.node.index)
		cur.move(RBNodeRight)
	}
}