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 (Python):
import sys


def main():
    x, y, z, k = [int(n) for n in input().split()]
    va = sorted([int(n) for n in input().split()], reverse=True)
    vb = sorted([int(n) for n in input().split()], reverse=True)
    xy = min(x*y, k)
    vab = (sorted([a + b for a in va for b in vb], reverse=True))[:xy]
    vc = sorted([int(n) for n in input().split()], reverse=True)
    xyz = min(x*y*z, k)
    print(*((sorted([ab + c for ab in vab for c in vc], reverse=True))[:xyz]), sep="\n")


main()

Solution (Python):
def main():
    X, Y, Z, K = map(int, input().split())
    A = list(map(int, input().split()))
    B = list(map(int, input().split()))
    C = list(map(int, input().split()))
    A.sort(reverse=True)
    B.sort(reverse=True)
    C.sort(reverse=True)

    T = []
    for a in A:
        for b in B:
            T.append(a + b)

    T = sorted(T, reverse=True)[:min(K, len(T))]

    res = []
    for t in T:
        for c in C:
            res.append(t + c)

    res = sorted(res, reverse=True)[:K]
    for r in res:
        print(r)

if __name__ == "__main__":
    main()

Solution (Python):
import heapq
def hq(x,y,z):
    return (-A[x-1]-B[y-1]-C[z-1],x,y,z)
X,Y,Z,K=map(int,input().split())
A=list(map(int,input().split()))
B=list(map(int,input().split()))
C=list(map(int,input().split()))
A.sort(reverse=True)
B.sort(reverse=True)
C.sort(reverse=True)

visited=[hq(1,1,1)]
ans=[]
q=[]
heapq.heappush(q,hq(1,1,1))
for _ in range(K):
    e,x,y,z=heapq.heappop(q)
    ans.append(-e)
    if x+1<=X and hq(x+1,y,z) not in visited:
        heapq.heappush(q,hq(x+1,y,z))
        visited.append(hq(x+1,y,z))
    if y+1<=Y and hq(x,y+1,z) not in visited:
        heapq.heappush(q,hq(x,y+1,z))
        visited.append(hq(x, y+1, z))
    if z+1<=Z and hq(x,y,z+1) not in visited:
        heapq.heappush(q,hq(x,y,z+1))
        visited.append(hq(x, y, z+1))

for i in ans:
    print(i)

Solution (Python):
import heapq
def hq(x,y,z):
    return (-A[x-1]-B[y-1]-C[z-1],x,y,z)
X,Y,Z,K=map(int,input().split())
A=list(map(int,input().split()))
B=list(map(int,input().split()))
C=list(map(int,input().split()))
A.sort(reverse=True)
B.sort(reverse=True)
C.sort(reverse=True)

visited=[hq(1,1,1)]
q=[]
heapq.heappush(q,hq(1,1,1))
for _ in range(K):
    e,x,y,z=heapq.heappop(q)
    if x+1<=X and hq(x+1,y,z) not in visited:
        heapq.heappush(q,hq(x+1,y,z))
        visited.append(hq(x+1,y,z))
    if y+1<=Y and hq(x,y+1,z) not in visited:
        heapq.heappush(q,hq(x,y+1,z))
        visited.append(hq(x, y+1, z))
    if z+1<=Z and hq(x,y,z+1) not in visited:
        heapq.heappush(q,hq(x,y,z+1))
        visited.append(hq(x, y, z+1))
visited.sort()
for i in visited[0:K]:
    print(-i[0])

Solution (Python):
import sys


def main():
    x, y, z, k = [int(n) for n in input().split()]
    va = sorted([int(n) for n in input().split()], reverse=True)
    vb = sorted([int(n) for n in input().split()], reverse=True)
    xy = min(x*y, k)
    vab = (sorted([a + b for a in va for b in vb], reverse=True))[:xy]
    vc = sorted([int(n) for n in input().split()], reverse=True)
    xyz = min(x*y*z, k)
    print(*((sorted([ab + c for ab in vab for c in vc], reverse=True))[:xyz]), sep="\n")


main()

Solution (Python):
X, Y, Z, K = map(int, input().split())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
C = list(map(int, input().split()))
A = sorted(A, reverse=True)
B = sorted(B, reverse=True)
C = sorted(C, reverse=True)

D = []
for i in range(X):
    for j in range(Y):
        D.append(A[i] + B[j])

D.sort(reverse=True)
E = []
for i in range(min(K, len(D))):
    for j in range(Z):
        E.append(D[i] + C[j])

E.sort(reverse=True)
for i in range(K):
    print(E[i])

Solution (Python):
from heapq import heappush, heappop
def main():
    X, Y, Z, K = map(int, input().split())
    a_cake = [int(x) for x in input().split()]
    b_cake = [int(x) for x in input().split()]
    c_cake = [int(x) for x in input().split()]

    a_cake.sort(reverse = True)
    b_cake.sort(reverse = True)
    c_cake.sort(reverse = True)

    heap_queue = []
    arg_hash = {}
    score_taste = a_cake[0] + b_cake[0] + c_cake[0]
    heappush(heap_queue, (-score_taste, 0, 0, 0))

    for i in range(K):
        score, a_candle, b_candle, c_candle = heappop(heap_queue)
        print(-score)

        arg_a = (a_candle+1, b_candle, c_candle)
        arg_b = (a_candle, b_candle+1, c_candle)
        arg_c = (a_candle, b_candle, c_candle+1)

        if a_candle < X-1 and arg_a not in arg_hash:
            arg_hash[arg_a] = 1
            heappush(heap_queue, (-(a_cake[a_candle+1] + b_cake[b_candle] + c_cake[c_candle]),) + arg_a)
        if b_candle < Y -1 and arg_b not in arg_hash:
            arg_hash[arg_b] = 1
            heappush(heap_queue, (-(a_cake[a_candle] + b_cake[b_candle+1] + c_cake[c_candle]),) + arg_b)
        if c_candle < Z -1 and arg_c not in arg_hash:
            arg_hash[arg_c] = 1
            heappush(heap_queue, (-(a_cake[a_candle] + b_cake[b_candle] + c_cake[c_candle+1]),) + arg_c)

if __name__ == "__main__":
    main()

Solution (Python):

from heapq import heappush, heappop
def main():
    X, Y, Z, K = map(int, input().split())
    a_cake = [int(x) for x in input().split()]
    b_cake = [int(x) for x in input().split()]
    c_cake = [int(x) for x in input().split()]

    a_cake.sort(reverse = True)
    b_cake.sort(reverse = True)
    c_cake.sort(reverse = True)

    heap_queue = []
    arg_hash = {}
    score_taste = a_cake[0] + b_cake[0] + c_cake[0]
    heappush(heap_queue, (-score_taste, 0, 0, 0))

    for i in range(K):
        score, a_candle, b_candle, c_candle = heappop(heap_queue)
        print(-score)

        arg_a = (a_candle+1, b_candle, c_candle)
        arg_b = (a_candle, b_candle+1, c_candle)
        arg_c = (a_candle, b_candle, c_candle+1)

        if a_candle < X-1 and arg_a not in arg_hash:
            arg_hash[arg_a] = 1
            heappush(heap_queue, (-(a_cake[a_candle+1] + b_cake[b_candle] + c_cake[c_candle]),) + arg_a)
        if b_candle < Y -1 and arg_b not in arg_hash:
            arg_hash[arg_b] = 1
            heappush(heap_queue, (-(a_cake[a_candle] + b_cake[b_candle+1] + c_cake[c_candle]),) + arg_b)
        if c_candle < Z -1 and arg_c not in arg_hash:
            arg_hash[arg_c] = 1
            heappush(heap_queue, (-(a_cake[a_candle] + b_cake[b_candle] + c_cake[c_candle+1]),) + arg_c)

if __name__ == "__main__":
    main()

Solution (Python):
import sys


s2nn = lambda s: [int(c) for c in s.split(' ')]
ss2nn = lambda ss: [int(s) for s in ss]
ss2nnn = lambda ss: [s2nn(s) for s in ss]
i2s = lambda: sys.stdin.readline().rstrip()
i2n = lambda: int(i2s())
i2nn = lambda: s2nn(i2s())
ii2ss = lambda n: [sys.stdin.readline().rstrip() for _ in range(n)]
ii2nn = lambda n: ss2nn(ii2ss(n))
ii2nnn = lambda n: ss2nnn(ii2ss(n))

N = 10000
def tokey(i, j, k):
    return i*N*N + j*N + k
def dekey(n):
    i = int(n / N / N)
    j = int(n / N) % N
    k = n % N
    return i, j, k

def main():
    X, Y, Z, K = i2nn()
    A = i2nn()
    B = i2nn()
    C = i2nn()
    A.sort()
    A.reverse()
    B.sort()
    B.reverse()
    C.sort()
    C.reverse()
    Q = [(A[0] + B[0] + C[0], 0, 0, 0)]
    loop = 0
    stored = set()
    def next(i, j, k):
        if i >= X or j >= Y or k >= Z:
            return
        key = tokey(i, j, k)
        if key not in stored:
            stored.add(key)
            n = A[i] + B[j] + C[k]
            Q.append((n, i, j, k))
    while True:
        v = max(Q, key=lambda v: v[0])
        Q.remove(v)
        print(v[0])
        loop += 1
        if loop >= K:
            break
        next(v[1]+1, v[2], v[3])
        next(v[1], v[2]+1, v[3])
        next(v[1], v[2], v[3]+1)

main()

Solution (Python):
import sys


s2nn = lambda s: [int(c) for c in s.split(' ')]
ss2nn = lambda ss: [int(s) for s in ss]
ss2nnn = lambda ss: [s2nn(s) for s in ss]
i2s = lambda: sys.stdin.readline().rstrip()
i2n = lambda: int(i2s())
i2nn = lambda: s2nn(i2s())
ii2ss = lambda n: [sys.stdin.readline().rstrip() for _ in range(n)]
ii2nn = lambda n: ss2nn(ii2ss(n))
ii2nnn = lambda n: ss2nnn(ii2ss(n))

N = 10000
def tokey(i, j, k):
    return i*N*N + j*N + k
def dekey(n):
    i = int(n / N / N)
    j = int(n / N) % N
    k = n % N
    return i, j, k

def main():
    X, Y, Z, K = i2nn()
    A = i2nn()
    B = i2nn()
    C = i2nn()
    A.sort()
    A.reverse()
    B.sort()
    B.reverse()
    C.sort()
    C.reverse()
    Q = [(A[0] + B[0] + C[0], 0, 0, 0)]
    loop = 0
    stored = set()
    def next(i, j, k):
        if i >= X or j >= Y or k >= Z:
            return
        key = tokey(i, j, k)
        if key not in stored:
            stored.add(key)
            n = A[i] + B[j] + C[k]
            Q.append((n, i, j, k))
    while True:
        Q.sort(key=lambda v: v[0])
        v = Q.pop()
        print(v[0])
        loop += 1
        if loop >= K:
            break
        next(v[1]+1, v[2], v[3])
        next(v[1], v[2]+1, v[3])
        next(v[1], v[2], v[3]+1)

main()

Solution (Python):
from collections import Counter
from collections import deque
from functools import reduce
from pprint import pprint

import bisect
import copy
import fractions
import math
import random
import sys
import time
sys.setrecursionlimit(10**7)
INF = 10 ** 18
MOD = 10 ** 9 + 7
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def MI(): return map(int, sys.stdin.readline().split())
def II(): return int(sys.stdin.readline())
def IS(): return input()
def C(x): return Counter(x)
def GCD_LIST(numbers): return reduce(fractions.gcd, numbers)
def LCM_LIST(numbers): return reduce(LCM, numbers)
def LCM(m, n): return (m * n // fractions.gcd(m, n))
def unite(x, y):
    
    x = root(x)
    y = root(y)
    if x == y:
        return
    
    node[x] = y
def same(x,y): return bool(root(x) == root(y))
def root(x):
    if node[x] == x:  
        return x
    else:
        node[x] = root(node[x])  
        return node[x]
def dfs(v):
    
    visited[v] = True
    for v2 in range(n):
        if graph[v][v2] == False:  
            continue
        if visited[v2] == True:  
            continue
        dfs(v2)


x, y, z, k = MI()
a = LI()
b = LI()
c = LI()
tmp = []
ans = []
for i in a:
    for j in b:
        tmp.append(i+j)
tmp = sorted(tmp, reverse=True)
for p in tmp[:k]:
    for q in c:
        ans.append(p+q)
ans = sorted(ans, reverse=True)
for num in ans[:k]:
    print(num)

Solution (Python):
X,Y,Z,K=map(int,input().split())
A=list(map(int,input().split()))
B=list(map(int,input().split()))
C=list(map(int,input().split()))
A.sort(reverse=True)
B.sort(reverse=True)
C.sort(reverse=True)
ans=[]
for i in range(X):
	j=0
	while((i+1)*(j+1)<K+1 and j<Y):
		k=0
		while((i+1)*(j+1)*(k+1)<K+1 and k<Z):
			ans.append(A[i]+B[j]+C[k])
			k+=1
		j+=1
ans.sort(reverse=True)
for i in range(K):
    print(ans[i])

Solution (Python):
import sys
input = sys.stdin.readline
'''
allinputs = iter(input().splitlines())
input = lambda : next(allinputs)


X, Y, Z, K = map(int, input().split())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
C = list(map(int, input().split()))

ans = []
tmp = []

for i in A:
	for j in B:
		tmp.append(i + j)
		
tmp.sort(reverse=True)

for i in range(min(K, len(tmp))):
	for j in C:
		ans.append(tmp[i] + j)
		
ans.sort(reverse=True)

for i in range(K):
	print(ans[i])

Solution (Python):


from heapq import heappush, heappop

X, Y, Z, K = map(int,input().split())
A = list(map(int,input().split()))
B = list(map(int,input().split()))
C = list(map(int,input().split()))

A.sort(reverse=True)
B.sort(reverse=True)
C.sort(reverse=True)

solver = []
hq = []
heappush(hq, (-(A[0]+B[0]+C[0]), 0, 0, 0))
for i in range(K):
  val, idx_a, idx_b, idx_c = heappop(hq)
  solver.append(-val)
  if idx_a + 1 < X:
    new_tuple_a = (-(A[idx_a+1]+B[idx_b]+C[idx_c]),idx_a+1,idx_b,idx_c)
    if new_tuple_a not in hq:
      heappush(hq, new_tuple_a)
  if idx_b + 1 < Y:
    new_tuple_b = (-(A[idx_a]+B[idx_b+1]+C[idx_c]),idx_a,idx_b+1,idx_c)
    if new_tuple_b not in hq:
      heappush(hq, new_tuple_b)
  if idx_c + 1 < Z:
    new_tuple_c = (-(A[idx_a]+B[idx_b]+C[idx_c+1]),idx_a,idx_b,idx_c+1)
    if new_tuple_c not in hq:
      heappush(hq, new_tuple_c)

for i in range(K):
  print(solver[i])

Solution (Python):
def intinput(): return map(int,input().split())

x,y,z,k=intinput()
a = list(intinput())
b = list(intinput())
c = list(intinput())
a.sort(reverse=1)
b.sort(reverse=1)
c.sort(reverse=1)
abc=[]
for i in range(x):
    for j in range(y):
        if (i+1)*(j+1)>k:
            break
        for l in range(z):
            if (i+1)*(j+1)*(l+1)>k:
                break
            abc.append(a[i]+b[j]+c[l])
abc.sort(reverse=1)
for i in range(k):
    print(abc[i])

Solution (Python):
import sys, os
from queue import PriorityQueue

f = lambda:list(map(int,input().split()))
if 'local' in os.environ :
    sys.stdin = open('./input.txt', 'r')

x, y, z, k = f()

def merge(a, b):
    q = PriorityQueue()
    ans = []

    for i in range(len(a)):
        q.put((-a[i] - b[0], 0))


    for i in range(min(k, len(a)*len(b))):
        cur = q.get()
        ans.append(-cur[0])
        idx = cur[1]
        if cur[1] + 1<len(b):
            q.put(( cur[0]+ b[idx] - b[idx+1] , cur[1] + 1))
    return ans

def solve():
    a = f()
    b = f()
    c = f()


    a = sorted(a, reverse = True)
    b = sorted(b, reverse = True)
    c = sorted(c, reverse = True)

    ans = merge(a,b)
    ans = merge(ans,c)

    for i in ans:
        print(i)


solve()

Solution (Python):



X, Y, Z, K = map(int, input().split())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
C = list(map(int, input().split()))

import heapq
import sys

INT_MIN = -1 * sys.maxsize

a_cakes = A[:]
a_cakes = sorted(a_cakes, reverse=True)
b_cakes = B[:]
b_cakes = sorted(b_cakes, reverse=True)
c_cakes = C[:]
c_cakes = sorted(c_cakes, reverse=True)


checked_dict = {'0_0_0': True}

a = a_cakes[0]
b = b_cakes[0]
c = c_cakes[0]
value_list = [(-a-b-c, (0, 0, 0))]
heapq.heapify(value_list)

for _ in range(K):
    val = heapq.heappop(value_list)
    print(-1*val[0])
    
    index = (val[1][0]+1, val[1][1], val[1][2])
    key = '{}_{}_{}'.format(*index)
    if not key in checked_dict:
        if not a_cakes[index[0]: index[0]+1]:
            continue
        checked_dict[key] = True
        a = a_cakes[index[0]]
        b = b_cakes[index[1]]
        c = c_cakes[index[2]]
        heapq.heappush(value_list, (-a-b-c, index))
        
    index = (val[1][0], val[1][1]+1, val[1][2])
    key = '{}_{}_{}'.format(*index)
    if not key in checked_dict:
        if not b_cakes[index[1]: index[1]+1]:
            continue
        checked_dict[key] = True
        a = a_cakes[index[0]]
        b = b_cakes[index[1]]
        c = c_cakes[index[2]]
        heapq.heappush(value_list, (-a-b-c, index))
        
    index = (val[1][0], val[1][1], val[1][2]+1)
    key = '{}_{}_{}'.format(*index)
    if not key in checked_dict:
        if not c_cakes[index[2]: index[2]+1]:
            continue
        checked_dict[key] = True
        a = a_cakes[index[0]]
        b = b_cakes[index[1]]
        c = c_cakes[index[2]]
        heapq.heappush(value_list, (-a-b-c, index))

Solution (Python):
import sys
stdin = sys.stdin

sys.setrecursionlimit(10 ** 7)

def li(): return map(int, stdin.readline().split())
def li_(): return map(lambda x: int(x) - 1, stdin.readline().split())
def lf(): return map(float, stdin.readline().split())
def ls(): return stdin.readline().split()
def ns(): return stdin.readline().rstrip()
def lc(): return list(ns())
def ni(): return int(stdin.readline())
def nf(): return float(stdin.readline())

from heapq import heappush, heappop
from collections import defaultdict

x, y, z, k = li()
a = list(li())
b = list(li())
c = list(li())

a.sort(reverse=True)
b.sort(reverse=True)
c.sort(reverse=True)

amax = a[0]
bmax = b[0]
cmax = c[0]

acnt = 0
bcnt = 0
ccnt = 0

heap = [(-amax - bmax - cmax, acnt, bcnt, ccnt)]
ans = []

visited = defaultdict(int)
visited[(0,0,0)] = 1

for _ in range(k):
    cur, acnt, bcnt, ccnt = heappop(heap)

    if acnt < len(a)-1:
        if not visited[(acnt+1, bcnt, ccnt)]:
            heappush(heap, (-a[acnt+1]-b[bcnt]-c[ccnt], acnt+1, bcnt, ccnt))
            visited[(acnt+1, bcnt, ccnt)] = 1

    if bcnt < len(b)-1:
        if not visited[(acnt, bcnt+1, ccnt)]:
            heappush(heap, (-a[acnt]-b[bcnt+1]-c[ccnt], acnt, bcnt+1, ccnt))
            visited[(acnt, bcnt+1, ccnt)] = 1

    if ccnt < len(c)-1:
        if not visited[(acnt, bcnt, ccnt+1)]:
            heappush(heap, (-a[acnt]-b[bcnt]-c[ccnt+1], acnt, bcnt, ccnt+1))
            visited[(acnt, bcnt, ccnt+1)] = 1

    ans.append(-cur)

for ansi in ans:
    print(ansi)

Solution (Python):

















import math
import copy
from collections import defaultdict
from collections import Counter
from collections import deque

from itertools import product

from itertools import permutations

from itertools import combinations
from bisect import bisect_left, bisect_right


def inside(y, x, H, W):
    return 0 <= y < H and 0 <= x < W


dy = [0, -1, 0, 1]
dx = [1, 0, -1, 0]

def i_inpl(): return int(input())
def s_inpl(): return map(int,input().split())
def l_inpl(): return list(map(int, input().split()))
INF = float("inf")
MAX_DIGIT = 50





X, Y, Z, K = l_inpl()
A = l_inpl()
B = l_inpl()
C = l_inpl()

top_k_AB = []
for i in range(X):
    for j in range(Y):
        top_k_AB.append(A[i] + B[j])

top_k_AB.sort(reverse=True)
top_k_AB = top_k_AB[:K]

top_k_ABC = []
for i in range(len(top_k_AB)):
    for j in range(Z):
        top_k_ABC.append(top_k_AB[i]+C[j])

top_k_ABC.sort(reverse=True)
print("\n".join([ str(s) for s in top_k_ABC[:K]]))

Solution (Python):
X, Y, Z, K = list(map(int, input().split()))
A = list(map(int, input().split()))
B = list(map(int, input().split()))
C = list(map(int, input().split()))

C = sorted(C, reverse=True)
AB = sorted([a + b for a in A for b in B], reverse=True)

ABC_k = sorted([ab + c for ab in AB[:K] for c in C], reverse=True)

for ans in ABC_k[:K]:
    print(ans)

Solution (Python):
x,y,z,k=map(int,input().split())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
c=list(map(int,input().split()))

ab=[]
for i in range(x):
    for j in range(y):
        ab.append(a[i]+b[j])
ab.sort()
aa=[]
for i in range(k):
    if x*y-i-1>=0:
        aa.append(ab[x*y-i-1])
ans=[]
for i in range(len(aa)):
    for j in range(z):
        ans.append(aa[i]+c[j])
ans.sort()
for i in range(k):
    print(ans[len(ans)-i-1])

Solution (Python):
def get_input():
    X, Y, Z, K = [int(_) for _ in raw_input().split()]
    A = [int(_) for _ in raw_input().split()]
    B = [int(_) for _ in raw_input().split()]
    C = [int(_) for _ in raw_input().split()]
    return X, Y, Z, K, A, B, C

def AddToQueue(_ele, _queue, _ijk_set, K):
    if len(_queue) == 0:
        _queue.append(_ele)
    else:
        cnt = 0
        while cnt < len(_queue) and _queue[cnt][0] >= _ele[0]:
            cnt += 1
        ijk = (_ele[1], _ele[2], _ele[3])
        if not (ijk in _ijk_set):
            _queue.insert(cnt, _ele)
            _ijk_set.add(ijk)
            _queue = _queue[:K]

def solve3():
    X, Y, Z, K, A, B, C = get_input()
    A.sort(reverse = True)
    B.sort(reverse = True)
    C.sort(reverse = True)
    ijk_set = set()
    queue = [(A[0] + B[0] + C[0], 0, 0, 0)]
    ijk_set.add((0, 0, 0))
    for cnt in range(K):
        ele, i, j, k = queue.pop(0)
        print ele
        if i + 1 < X:
            AddToQueue((A[i+1] + B[j] + C[k], i+1, j, k), queue, ijk_set, K)
        if j + 1 < Y:
            AddToQueue((A[i] + B[j+1] + C[k], i, j+1, k), queue, ijk_set, K)
        if k + 1 < Z:
            AddToQueue((A[i] + B[j] + C[k+1], i, j, k+1), queue, ijk_set, K)

if __name__ == '__main__':
    solve3()

Solution (Python):
x, y, z, k = map(int, input().split())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
c = list(map(int, input().split()))

a.sort()
a.reverse()
b.sort()
b.reverse()
c.sort(reverse=True)
ans = []

for n in range(len(a)):
    for m in range(len(b)):
        if (n+1)*(m+1) > k:
            break
        for l in range(len(c)):
            if (n+1)*(m+1)*(l+1) > k:
                break
            ans.append(a[n]+b[m]+c[l])

ans.sort(reverse=True)
for i in range(k):
    print(ans[i])

Solution (Python):
def MergeSort(arr):
    if len(arr) <= 1:
        return arr
    mid = len(arr) // 2
    left = arr[:mid]
    right = arr[mid:]
    left = MergeSort(left)
    right = MergeSort(right)
    return MergeArray(left, right)

def MergeArray(left, right):
    merged = []
    li, ri = 0, 0
    while li < len(left) and ri < len(right):
        if left[li] > right[ri]:
            merged.append(left[li])
            li += 1
        else:
            merged.append(right[ri])
            ri += 1
    if li < len(left):
        merged.extend(left[li:])
    elif ri < len(right):
        merged.extend(right[ri:])
    return merged

def solve():
    X, Y, Z, K = [int(_) for _ in raw_input().split()]
    A = [int(_) for _ in raw_input().split()]
    B = [int(_) for _ in raw_input().split()]
    C = [int(_) for _ in raw_input().split()]
    A = MergeSort(A)[:K]
    B = MergeSort(B)[:K]
    C = MergeSort(C)[:K]
    lB = len(B)
    lC = len(C)
    sumAB = []
    for i in range(lB):
        tmpA = [ele + B[i] for ele in A]
        sumAB = MergeArray(sumAB, tmpA)[:K]
    sumABC = []
    for i in range(lC):
        tmpAB = [ele + C[i] for ele in sumAB]
        sumABC = MergeArray(sumABC, tmpAB)[:K]
    for i in range(K):
        print sumABC[i]

if __name__ == '__main__':
    solve()

Solution (Python):
x,y,z,k=map(int,input().split())
A=[int(i) for i in input().split()]
B=[int(i) for i in input().split()]
C=[int(i) for i in input().split()]
a,b,c=0,0,0
AB=[]
for a in A:
  for b in B:
    AB.append(a+b)
AB.sort(reverse=True)
AB=AB[:k]
ABC=[]
for ab in AB:
  for c in C:
    ABC.append(ab+c)
ABC.sort(reverse=True)
print(*ABC[:k],sep="\n")

Solution (Python):
from collections import deque
X, Y, Z, K = map(int,input().split())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
C = list(map(int, input().split()))

out = deque()
out2 = deque()

for i in range(X):
    for j in range(Y):
        out.append(A[i]+B[j])
out = sorted(out, reverse=True)
del out[K:]
for i in range(len(out)):
    for j in range(Z):
        out2.append(out[i]+C[j])
out2 = sorted(out2, reverse=True)
for i in range(K):
    print(out2[i])

Solution (Python):
import numpy as np
import heapq





x,y,z,K = map(int, input().split())

li = [
    sorted(list(map(int, input().split()))),
    sorted(list(map(int, input().split()))),
    sorted(list(map(int, input().split()))),
]
cand = []

m = li[0][x-1] + li[1][y-1] + li[2][z-1]
heapq.heappush(cand, (-m, x-1, y-1, z-1))
memo = set()
res = 0

while res < K:
    m,i,j,k = heapq.heappop(cand)

    if (i,j,k) in memo:
        continue
    memo.add((i,j,k))
    print(-m)
    res += 1

    if i > 0:
        m = li[0][i-1] + li[1][j] + li[2][k]
        heapq.heappush(cand, (-m, i-1, j, k))
    if j > 0:
        m = li[0][i] + li[1][j-1] + li[2][k]
        heapq.heappush(cand, (-m, i, j-1, k))
    if k > 0:
        m = li[0][i] + li[1][j] + li[2][k-1]
        heapq.heappush(cand, (-m, i, j, k-1))

Solution (Python):
x,y,z,k = map(int, input().split())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
c = list(map(int, input().split()))

d = []
for xx in a:
    for yy in b:
        d.append(xx+yy)
d.sort()
d.reverse()


e = []
if len(d)>3000:
    for i in range(3000):
        for zz in c:
            e.append(d[i]+zz)
else:
    for xy in d:
        for zz in c:
            e.append(xy+zz)
e.sort()
e.reverse()

for i in range(k):
    print(e[i])

Solution (Python):
x, y, z, k = map(int,input().split())
a = list(map(int,input().split()))
b = list(map(int,input().split()))
c = list(map(int,input().split()))
a.sort(reverse = 1)
b.sort(reverse = 1)
c.sort(reverse = 1)

v = []

for p in range(x):
  for q in range(y):
    for r in range(z):
      if (p+1)*(q+1)*(r+1) > 3000:
        break
      v.append(a[p]+b[q]+c[r])

v.sort(reverse = 1)
for i in range(k):
  print(v[i])

Solution (Python):
import sys
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def II(): return int(sys.stdin.readline())
def LS(): return sys.stdin.readline().split()
sys.setrecursionlimit(10**7)
INF = 10 ** 18
MOD = 10 ** 9 + 7
def LI_(): return [int(x) - 1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def SI(): return input()
YN = lambda b: print('YES') if b else print('NO')
yn = lambda b: print('Yes') if b else print('No')

X, Y, Z, K = LI()
A_li = LI()
B_li = LI()
C_li = LI()

A_li = sorted(A_li, reverse=True) + [-INF]
B_li = sorted(B_li, reverse=True) + [-INF]
C_li = sorted(C_li, reverse=True) + [-INF]

from functools import lru_cache

@lru_cache(maxsize=None)
def calc_result(a,b,c):
    return (A_li[a]+B_li[b]+C_li[c])


search_list = [(0,0,0)]
calc_list = [calc_result(0,0,0)]
for i in range(K):
    maximum = max(calc_list)
    print(maximum)
    index = calc_list.index(maximum)
    a, b, c = search_list[index]
    search_list.pop(index)
    calc_list.pop(index)
    if (a+1, b, c) not in search_list:
        search_list.append((a+1,b,c))
        calc_list.append(calc_result(a+1,b,c))
    if (a, b+1, c) not in search_list:
        search_list.append((a,b+1,c))
        calc_list.append(calc_result(a,b+1,c))
    if (a, b, c+1) not in search_list:
        search_list.append((a,b,c+1))
        calc_list.append(calc_result(a,b,c+1))

Solution (Python):
x,y,z,K = map(int, input().split())

a = list(map(int, input().split()))
b = list(map(int, input().split()))
c = list(map(int, input().split()))
a.sort(reverse=True)
b.sort(reverse=True)
c.sort(reverse=True)

abc = []

for i in range (x):
      for j in range(y):
            for(k) in range(z):
                  if (i+1)*(j+1)*(k+1) <= K:
                        abc.append(a[i]+b[j]+c[k])
                  else:
                        break

abc.sort(reverse=True)
for i in abc[:K]:
      print(i)

Solution (Python):
X,Y,Z,K=map(int,input().split())
def INPUT():
    ans=list(map(int,input().split()))
    ans.sort(reverse=True)
    return ans
A=INPUT()
B=INPUT()
C=INPUT()
ans=[]
for i in range(1,1+X):
    for j in range(1,1+Y):
        if i*j-1>=K:
            break
        for k in range(1,1+Z):
            if i*j*k-1>=K:
                break
            ans+=[A[i-1]+B[j-1]+C[k-1]]
ans.sort(reverse=True)
for i in range(K):
    print(ans[i])

Solution (Python):
from queue import PriorityQueue

def sub():
    lines = [input() for _ in range(4)]
    X, Y, Z, K = [int(e) for e in lines[0].split(" ")]
    As = [int(e) for e in lines[1].split(" ")]
    Bs = [int(e) for e in lines[2].split(" ")]
    Cs = [int(e) for e in lines[3].split(" ")]

    As = sorted(As, reverse=True)
    Bs = sorted(Bs, reverse=True)
    Cs = sorted(Cs, reverse=True)
    nb_A = len(As)
    nb_B = len(Bs)
    nb_C = len(Cs)
    
    memSet = set()
    pq = PriorityQueue()
    pq.put_nowait(( -(As[0]+Bs[0]+Cs[0]), (0,0,0)))
    memSet.add((0,0,0))
    
    for i in range(K):
        v, q = pq.get_nowait()
        print(-v)

        a, b, c = q
        if a+1 < nb_A:
            qTmp = (a+1, b, c)
            if qTmp not in memSet:
                memSet.add(qTmp)
                item = (-(As[qTmp[0]] + Bs[qTmp[1]] + Cs[qTmp[2]]), qTmp)
                pq.put_nowait(item)
        if b+1 < nb_B:
            qTmp = (a, b+1, c)
            if qTmp not in memSet:
                memSet.add(qTmp)
                item = (-(As[qTmp[0]] + Bs[qTmp[1]] + Cs[qTmp[2]]), qTmp)
                pq.put_nowait(item)
        if c+1 < nb_C:
            qTmp = (a, b, c+1)
            if qTmp not in memSet:
                memSet.add(qTmp)
                item = (-(As[qTmp[0]] + Bs[qTmp[1]] + Cs[qTmp[2]]), qTmp)
                pq.put_nowait(item)

sub()

Solution (Python):
x,y,z,k = map(int,input().split())
lisa = list(map(int,input().split()))
lisb = list(map(int,input().split()))
lisc = list(map(int,input().split()))
lisa.sort(reverse=True)
lisb.sort(reverse=True)
lisc.sort(reverse=True)
an = []
ans = []
for num in lisb:
    for nu in lisa:
        an.append(num+nu)
an.sort(reverse=True)
an = an[:min(3001,x*y*z+1)]
for num in lisc:
    for nu in an:
        ans.append(num+nu)
ans.sort(reverse=True)
for i in range(k):
    print(ans[i])