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.



Sample input:
2 2 2 8
4 6
1 5
3 8


Sample output:
19
17
15
14
13
12
10
8

Submission status: Time Limit Exceeded

Solution code:
import sys
import heapq

input = sys.stdin.readline


def main():
    X, Y, Z, K = map(int, input().split())
    A = list(map(lambda x: -int(x), input().split()))
    B = list(map(lambda x: -int(x), input().split()))
    C = list(map(lambda x: -int(x), input().split()))

    A.sort()
    B.sort()
    C.sort()

    p_queue = [(A[0] + B[0] + C[0], 0, 0, 0)]
    appear = [[[False for _ in range(Z)] for _ in range(Y)] for _ in range(X)]
    appear[0][0][0] = True
    ans = []
    while len(ans) < K:
        s, i_A, i_B, i_C = heapq.heappop(p_queue)
        ans.append(-s)
        if i_A < X - 1 and not appear[i_A + 1][i_B][i_C]:
            appear[i_A + 1][i_B][i_C] = True
            t = s - A[i_A] + A[i_A + 1]
            p_queue.append((t, i_A + 1, i_B, i_C))
        if i_B < Y - 1 and not appear[i_A][i_B + 1][i_C]:
            appear[i_A][i_B + 1][i_C] = True
            t = s - B[i_B] + B[i_B + 1]
            p_queue.append((t, i_A, i_B + 1, i_C))
        if i_C < Z - 1 and not appear[i_A][i_B][i_C + 1]:
            appear[i_A][i_B][i_C + 1] = True
            t = s - C[i_C] + C[i_C + 1]
            p_queue.append((t, i_A, i_B, i_C + 1))

        heapq.heapify(p_queue)

    print("\n".join(map(str, ans)))


if __name__ == "__main__":
    main()

Submission status: Time Limit Exceeded

Solution code:
from heapq import heappop, heappush
def main():
    def push(i, j, k):
        nonlocal A, B, C, ADD
        if i >= x or j >= y or k >= z: return
        if not ADD[i][j][k]:
            heappush(H, (A[i] + B[j] + C[k], i, j, k))
            ADD[i][j][k] = True
    x, y, z, k = map(int, input().split())
    INF = 10 ** 11
    A = sorted(list(map(lambda x: -int(x), input().split())))
    B = sorted(list(map(lambda x: -int(x), input().split())))
    C = sorted(list(map(lambda x: -int(x), input().split())))
    H = []
    ADD = [[[False] * z for _ in range(y)] for _ in range(x)]
    push(0, 0, 0)
    for _ in range(k):
        ans, i, j, k = heappop(H)
        push(i + 1, j, k)
        push(i, j + 1, k)
        push(i, j, k + 1)
        print(-ans)

if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

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

AB = [0]*(X*Y)
i = 0
for a in A:
  for b in B:
    AB[i] = a+b
    i += 1
AB.sort(reverse = True)

ans = [0]*(K*Z)
j = 0
for ab in AB[:K]:
  for c in C:
    ans[j] = ab+c
    j += 1

ans.sort(reverse=True)
print(*ans[:K], sep="\n")

Submission status: Time Limit Exceeded

Solution code:
import sys
input = sys.stdin.readline

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

AB = []
for a in A:
  for b in B:
    AB.append(a+b)
AB.sort(reverse = True)

ans = []
for ab in AB[:K]:
  for c in C:
    ans.append(ab+c)

ans.sort(reverse=True)
print(*ans[:K], sep="\n")

Submission status: Time Limit Exceeded

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

AB = []
for a in A:
  for b in B:
    AB.append(a+b)
AB.sort(reverse = True)

ans = []
for ab in AB[:K]:
  for c in C:
    ans.append(ab+c)

ans.sort(reverse=True)
print(*ans[:K], sep="\n")

Submission status: Time Limit Exceeded

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

for i in A:
    for j in B:
        for k in C:
            s.append(i+j+k)

s = sorted(s, reverse=True)

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

Submission status: Time Limit Exceeded

Solution code:
import numpy as np
x,y,z,k = map(int,input().split())
a = np.array(list(map(int, input().split())))
b = np.array(list(map(int, input().split())))
c = np.array(list(map(int, input().split())))
ans = []
for i in range(x):
    for j in range(y):
        for l in range(z):
            ans.append(a[i] + b[j] + c[l])
ans.sort(reverse = True)
for i in range(k):
    print(ans[i])

Submission status: Time Limit Exceeded

Solution code:
import sys

sys.setrecursionlimit(10 ** 7)
input = sys.stdin.readline
f_inf = float('inf')
mod = 10 ** 9 + 7


def resolve():
    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(reverse=True)

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

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


if __name__ == '__main__':
    resolve()

Submission status: Time Limit Exceeded

Solution code:
import sys

sys.setrecursionlimit(10 ** 7)
input = sys.stdin.readline
f_inf = float('inf')
mod = 10 ** 9 + 7


def resolve():
    X, Y, Z, K = map(int, input().split())
    A = sorted(list(map(int, input().split())), reverse=True)
    B = sorted(list(map(int, input().split())), reverse=True)
    C = sorted(list(map(int, input().split())), reverse=True)
    MAX = 500

    res = []
    for i in range(min(len(A), MAX)):
        for j in range(min(len(B), MAX)):
            for k in range(min(len(C), MAX)):
                res.append(A[i] + B[j] + C[k])
    res.sort(reverse=True)
    for i in range(K):
        print(res[i])


if __name__ == '__main__':
    resolve()

Submission status: Time Limit Exceeded

Solution code:
from bisect import bisect_left

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()))

if X*Y*Z <= 10**10:
  D = sorted([A[i]+B[j]+C[k] for i in range(X) for j in range(Y) for k in range(Z)],reverse=True)
  for i in range(K):
    print(D[i])
  
else:
  A = sorted(A)
  D = sorted([B[i]+C[j] for i in range(Y) for j in range(Z)])

  thr = K
  s = A[-1]+D[max(0,len(D)-thr)]
  prev_idx=0
  selected = [A[-1] + D[i] for i in range(len(D))]
  for i in range(1,X):
    r = s - A[-1-i]
    if r<=0:break
    idx = bisect_left(D,r,prev_idx,len(D)-1)
    if idx == len(D):break
    selected.extend([A[-1-i] + D[j] for j in range(idx,len(D))])
    prec_idx = idx

  selected = sorted(selected,reverse=True)
  print(len(selected))

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

Submission status: Time Limit Exceeded

Solution code:
from bisect import bisect_left

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()))

if X*Y*Z <= 10**5:
  D = sorted([A[i]+B[j]+C[k] for i in range(X) for j in range(Y) for k in range(Z)],reverse=True)
  for i in range(K):
    print(D[i])
  
else:
  A = sorted(A)
  D = sorted([B[i]+C[j] for i in range(Y) for j in range(Z)])

  thr = K//2
  s = A[-1]+D[0]
  prev_idx=0
  selected = [A[-1] + D[i] for i in range(len(D))]
  for i in range(1,X):
    r = s - A[-1-i]
    if r<=0:break
    idx = bisect_left(D,r,prev_idx,len(D)-1)
    if idx == len(D):break
    selected.extend([A[-1-i] + D[j] for j in range(idx,len(D))])
    prec_idx = idx

  selected = sorted(selected,reverse=True)
  print(len(selected))

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

Submission status: Time Limit Exceeded

Solution code:
from bisect import bisect_left

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()))

if X*Y*Z <= 10**5:
  D = sorted([A[i]+B[j]+C[k] for i in range(X) for j in range(Y) for k in range(Z)],reverse=True)
  for i in range(K):
    print(D[i])
  
else:
  A = sorted(A)
  D = sorted([B[i]+C[j] for i in range(Y) for j in range(Z)])

  thr = K
  s = A[-1]+D[0]
  prev_idx=0
  selected = [A[-1] + D[i] for i in range(len(D))]
  for i in range(1,X):
    r = s - A[-1-i]
    if r<=0:break
    idx = bisect_left(D,r,prev_idx,len(D)-1)
    if idx == len(D):break
    selected.extend([A[-1-i] + D[j] for j in range(idx,len(D))])
    prec_idx = idx

  selected = sorted(selected,reverse=True)
  print(len(selected))

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

Submission status: Time Limit Exceeded

Solution code:
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)

done = {(i,j,k): False 
        for i in range(X+1) for j in range(Y+1) for k in range(Z+1)}
import heapq
q = [(-A[0]-B[0]-C[0],0,0,0)]
heapq.heapify(q)

for _ in range(K):
    ma,i,j,k = heapq.heappop(q)
    if not done[(i+1,j,k)] and i<X-1:
        done[(i+1,j,k)]=True
        heapq.heappush(q,(-A[i+1]-B[j]-C[k] , i+1,j,k))
    
    if not done[(i,j+1,k)] and j<Y-1:
        done[(i,j+1,k)]=True
        heapq.heappush(q,(-A[i]-B[j+1]-C[k] , i,j+1,k))
    
    if not done[(i,j,k+1)] and k<Z-1:
        done[(i,j,k+1)]=True
        heapq.heappush(q,(-A[i]-B[j]-C[k+1] , i,j,k+1))
    print(-ma)

Submission status: Time Limit Exceeded

Solution code:
from itertools import product

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()))

p = [i + k for i, k in product(a, b)]
p.sort(reverse=True)
q = [i + k for i, k in product(p[:k], c)]
q.sort(reverse=True)

print('\n'.join(map(str, q[:k])))

Submission status: Time Limit Exceeded

Solution code:
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 i in A:
  for j in B:
    D.append(i+j)
D=sorted(D)[::-1]
if X*Y>K:
  D=D[:K]
E=[]
for i in D:
  for j in C:
    E.append(i+j)
E=sorted(E)[::-1]
E=E[:K]
for i in E:
  print(i)

Submission status: Time Limit Exceeded

Solution code:
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()))
l = []
for i in a:
    for j in b:
        l.append(i + j)
c.sort(reverse=True)
l.sort(reverse=True)
l2 = []
for i in c:
    for j in l:
        l2.append(i + j)
l2.sort(reverse=True)
print(*l2[:k], sep="\n")

Submission status: Time Limit Exceeded

Solution code:
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()))

ABC = []
for a in A:
    for b in B:
        for c in C:
            ABC.append(a+b+c)
ABC = sorted(ABC,reverse=True)
for k in range(K):
    print(ABC[k])

Submission status: Time Limit Exceeded

Solution code:
import itertools

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

AB = [a + b for (a, b) in list(itertools.product(A, B))]
AB.sort(reverse = True)
ans = [ab + c for (ab, c) in list(itertools.product(AB[:K], C))]
ans.sort(reverse = True)

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

Submission status: Time Limit Exceeded

Solution code:
import itertools

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

AB = [a + b for (a, b) in list(itertools.product(A, B))]
AB.sort(reverse = True)
ans = [ab + c for (ab, c) in list(itertools.product(AB[:min(3000, X*Y*Z)], C))]
ans.sort(reverse = True)

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

Submission status: Time Limit Exceeded

Solution code:
import itertools

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()))

AB = [a + b for (a, b) in list(itertools.product(A, B))]
AB.sort(reverse = True)
ans = [ab + c for (ab, c) in list(itertools.product(AB[:min(3000, X*Y*Z)], C))]
ans.sort(reverse = True)

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

Submission status: Time Limit Exceeded

Solution code:
import heapq

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)

hq = [[-a[0]-b[0]-c[0], 0, 0, 0]]
heapq.heapify(hq)
visited = [[[0] * z for yy in range(y)] for xx in range(x)]
for i in range(k):
    ii, ia, ib, ic = heapq.heappop(hq)
    print(-ii)
    na = min(ia+1, x-1)
    nb = min(ib+1, y-1)
    nc = min(ic+1, z-1)
    if visited[na][ib][ic] == 0:
        heapq.heappush(hq, [-a[na] -b[ib] -c[ic], na, ib, ic])
        visited[na][ib][ic] = 1
    if visited[ia][nb][ic] == 0:
        heapq.heappush(hq, [-a[ia] -b[nb] -c[ic], ia, nb, ic])
        visited[ia][nb][ic] = 1
    if visited[ia][ib][nc] == 0:
        heapq.heappush(hq, [-a[ia] -b[ib] -c[nc], ia, ib, nc])
        visited[ia][ib][nc] = 1

Submission status: Time Limit Exceeded

Solution code:
import heapq

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)

hq = [[-a[0]-b[0]-c[0], 0, 0, 0]]
heapq.heapify(hq)
visited = [[[0] * z for yy in range(y)] for xx in range(x)]
for i in range(k):
    ii, ia, ib, ic = heapq.heappop(hq)
    print(-ii)
    na = min(ia+1, x-1)
    nb = min(ib+1, y-1)
    nc = min(ic+1, z-1)
    if visited[na][ib][ic] == 0:
        heapq.heappush(hq, [-a[na] -b[ib] -c[ic], na, ib, ic])
        visited[na][ib][ic] = 1
    if visited[ia][nb][ic] == 0:
        heapq.heappush(hq, [-a[ia] -b[nb] -c[ic], ia, nb, ic])
        visited[ia][nb][ic] = 1
    if visited[ia][ib][nc] == 0:
        heapq.heappush(hq, [-a[ia] -b[ib] -c[nc], ia, ib, nc])
        visited[ia][ib][nc] = 1

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-

#############
# Libraries #
#############

import sys
input = sys.stdin.readline

import math
#from math import gcd
import bisect
import heapq
from collections import defaultdict
from collections import deque
from collections import Counter
from functools import lru_cache

#############
# Constants #
#############

MOD = 10**9+7
INF = float('inf')
AZ = "abcdefghijklmnopqrstuvwxyz"

#############
# Functions #
#############

######INPUT######
def I(): return int(input().strip())
def S(): return input().strip()
def IL(): return list(map(int,input().split()))
def SL(): return list(map(str,input().split()))
def ILs(n): return list(int(input()) for _ in range(n))
def SLs(n): return list(input().strip() for _ in range(n))
def ILL(n): return [list(map(int, input().split())) for _ in range(n)]
def SLL(n): return [list(map(str, input().split())) for _ in range(n)]

######OUTPUT######
def P(arg): print(arg); return
def Y(): print("Yes"); return
def N(): print("No"); return
def E(): exit()
def PE(arg): print(arg); exit()
def YE(): print("Yes"); exit()
def NE(): print("No"); exit()

#####Shorten#####
def DD(arg): return defaultdict(arg)

#####Inverse#####
def inv(n): return pow(n, MOD-2, MOD)

######Combination######
kaijo_memo = []
def kaijo(n):
  if(len(kaijo_memo) > n): return kaijo_memo[n]
  if(len(kaijo_memo) == 0): kaijo_memo.append(1)
  while(len(kaijo_memo) <= n): kaijo_memo.append(kaijo_memo[-1] * len(kaijo_memo) % MOD)
  return kaijo_memo[n]

gyaku_kaijo_memo = []
def gyaku_kaijo(n):
  if(len(gyaku_kaijo_memo) > n): return gyaku_kaijo_memo[n]
  if(len(gyaku_kaijo_memo) == 0): gyaku_kaijo_memo.append(1)
  while(len(gyaku_kaijo_memo) <= n): gyaku_kaijo_memo.append(gyaku_kaijo_memo[-1] * pow(len(gyaku_kaijo_memo),MOD-2,MOD) % MOD)
  return gyaku_kaijo_memo[n]

def nCr(n,r):
  if n == r: return 1
  if n < r or r < 0: return 0
  ret = 1
  ret = ret * kaijo(n) % MOD
  ret = ret * gyaku_kaijo(r) % MOD
  ret = ret * gyaku_kaijo(n-r) % MOD
  return ret

######Factorization######
def factorization(n):
  arr = []
  temp = n
  for i in range(2, int(-(-n**0.5//1))+1):
    if temp%i==0:
      cnt=0
      while temp%i==0: 
        cnt+=1 
        temp //= i
      arr.append([i, cnt])
  if temp!=1: arr.append([temp, 1])
  if arr==[]: arr.append([n, 1])
  return arr

#####MakeDivisors######
def make_divisors(n):
  divisors = []
  for i in range(1, int(n**0.5)+1):
    if n % i == 0:
      divisors.append(i)
      if i != n // i: 
        divisors.append(n//i)
  return divisors

#####MakePrimes######
def make_primes(N):
  max = int(math.sqrt(N))
  seachList = [i for i in range(2,N+1)]
  primeNum = []
  while seachList[0] <= max:
    primeNum.append(seachList[0])
    tmp = seachList[0]
    seachList = [i for i in seachList if i % tmp != 0]
  primeNum.extend(seachList)
  return primeNum

#####GCD#####
def gcd(a, b):
    while b: a, b = b, a % b
    return a

#####LCM#####
def lcm(a, b):
    return a * b // gcd (a, b)

#####BitCount#####
def count_bit(n):
  count = 0
  while n:
    n &= n-1
    count += 1
  return count

#####ChangeBase#####
def base_10_to_n(X, n):
  if X//n: return base_10_to_n(X//n, n)+[X%n]
  return [X%n]

def base_n_to_10(X, n):
  return sum(int(str(X)[-i-1])*n**i for i in range(len(str(X))))

def base_10_to_n_without_0(X, n):
  X -= 1
  if X//n: return base_10_to_n_without_0(X//n, n)+[X%n]
  return [X%n]

#####IntLog#####
def int_log(n, a):
  count = 0
  while n>=a:
    n //= a
    count += 1
  return count

#############
# Main Code #
#############

X,Y,Z,K = IL()
A = IL()
B = IL()
C = IL()
A.sort(reverse = True)
B.sort(reverse = True)
C.sort(reverse = True)

ans = []
q = [(-A[0]-B[0]-C[0],0,0,0)]
f = [[[0 for z in range(Z)] for y in range(Y)] for x in range(X)]
dx = [-1,1,0,0,0,0]
dy = [0,0,-1,1,0,0]
dz = [0,0,0,0,-1,1,]
f[0][0][0] = 1
while K:
  K -= 1
  v,x,y,z = heapq.heappop(q)
  ans.append(-v)
  for i in range(6):
    nx,ny,nz = x+dx[i],y+dy[i],z+dz[i]
    if nx<0 or nx>=X or ny<0 or ny>=Y or nz<0 or nz>=Z: continue
    if f[nx][ny][nz]: continue
    heapq.heappush(q,(-A[nx]-B[ny]-C[nz],nx,ny,nz))
    f[nx][ny][nz] = 1
  
for a in ans:
  print(a)

Submission status: Time Limit Exceeded

Solution code:
numx,numy,numz,k=list(map(int,input().split()))
X=list(map(int,input().split()))
Y=list(map(int,input().split()))
Z=list(map(int,input().split()))

XY=[ x + y for x in X for y in Y]
XY.sort(reverse=True)
XY=XY[:k]
XYZ=[xy + z for xy in XY for z in Z]
XYZ.sort(reverse=True)

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

Submission status: Time Limit Exceeded

Solution code:
# coding: utf-8
# hello worldと表示する
#float型を許すな
#numpyはpythonで
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**7)
from collections import Counter, deque
from collections import defaultdict
from itertools import combinations, permutations, accumulate, groupby, product
from bisect import bisect_left,bisect_right
from heapq import heapify, heappop, heappush
from math import floor, ceil,pi,factorial
from operator import itemgetter
def I(): return int(input())
def MI(): return map(int, input().split())
def LI(): return list(map(int, input().split()))
def LI2(): return [int(input()) for i in range(n)]
def MXI(): return [[LI()]for i in range(n)]
def SI(): return input().rstrip()
def printns(x): print('\n'.join(x))
def printni(x): print('\n'.join(list(map(str,x))))
inf = 10**17
mod = 10**9 + 7

def main():
    x,y,z,k=MI()
    A=sorted(LI(),reverse=True)
    B=sorted(LI(),reverse=True)
    C=sorted(LI(),reverse=True)
    Q=[[(A[0]+B[0]+C[0])*(-1),0,0,0]]
    heapify(Q)
    #print(Q)
    i=0
    ans=[]
    #print(heappop(Q))
    #al=[[[-1]*x for i in range(y)] for j in range(z)]
    #al[0][0][0]=0
    xl,yl,zl=0,0,0
    al=[]
    al=[[0,0,0]]
    while i<k:
        #print(Q)
        if not Q:
            sys.exit()
        a,u,v,w=heappop(Q)
        ans.append(-a)
        i+=1
        if u+1<x and (not ([u+1,v,w] in al)):
            heappush(Q,[-A[u+1]-B[v]-C[w],u+1,v,w])
            al.append([u+1,v,w])
            
            #al[u+1][v][w]=0
        if v+1<y and not([u,v+1,w] in al):
            heappush(Q,[-A[u]-B[v+1]-C[w],u,v+1,w])
            al.append([u,v+1,w])
            #al[u][v+1][w]=0
        if w+1<z and not([u,v,w+1] in al):
            heappush(Q,[-A[u]-B[v]-C[w+1],u,v,w+1])
            al.append([u,v,w+1])
    #print(len(ans))
    for i in range(k):
        print(ans[i])
if __name__=="__main__":
    main()

Submission status: Time Limit Exceeded

Solution code:
# coding: utf-8
# hello worldと表示する
#float型を許すな
#numpyはpythonで
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**7)
from collections import Counter, deque
from collections import defaultdict
from itertools import combinations, permutations, accumulate, groupby, product
from bisect import bisect_left,bisect_right
from heapq import heapify, heappop, heappush
from math import floor, ceil,pi,factorial
from operator import itemgetter
def I(): return int(input())
def MI(): return map(int, input().split())
def LI(): return list(map(int, input().split()))
def LI2(): return [int(input()) for i in range(n)]
def MXI(): return [[LI()]for i in range(n)]
def SI(): return input().rstrip()
def printns(x): print('\n'.join(x))
def printni(x): print('\n'.join(list(map(str,x))))
inf = 10**17
mod = 10**9 + 7

x,y,z,k=MI()
A=sorted(LI(),reverse=True)
B=sorted(LI(),reverse=True)
C=sorted(LI(),reverse=True)
Q=[[(A[0]+B[0]+C[0])*(-1),0,0,0]]
heapify(Q)
#print(Q)
i=0
ans=[]
#print(heappop(Q))
#al=[[[-1]*x for i in range(y)] for j in range(z)]
#al[0][0][0]=0
xl,yl,zl=0,0,0
al=[]
al=[[0,0,0]]
while i<k:
    #print(Q)
    if not Q:
        sys.exit()
    a,u,v,w=heappop(Q)
    ans.append(-a)
    i+=1
    if u+1<x and (not ([u+1,v,w] in al)):
        heappush(Q,[-A[u+1]-B[v]-C[w],u+1,v,w])
        al.append([u+1,v,w])
        
        #al[u+1][v][w]=0
    if v+1<y and not([u,v+1,w] in al):
        heappush(Q,[-A[u]-B[v+1]-C[w],u,v+1,w])
        al.append([u,v+1,w])
        #al[u][v+1][w]=0
    if w+1<z and not([u,v,w+1] in al):
        heappush(Q,[-A[u]-B[v]-C[w+1],u,v,w+1])
        al.append([u,v,w+1])
#print(len(ans))
for i in range(k):
    print(ans[i])

Submission status: Time Limit Exceeded

Solution code:
# coding: utf-8
# hello worldと表示する
#float型を許すな
#numpyはpythonで
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**7)
from collections import Counter, deque
from collections import defaultdict
from itertools import combinations, permutations, accumulate, groupby, product
from bisect import bisect_left,bisect_right
from heapq import heapify, heappop, heappush
from math import floor, ceil,pi,factorial
from operator import itemgetter
def I(): return int(input())
def MI(): return map(int, input().split())
def LI(): return list(map(int, input().split()))
def LI2(): return [int(input()) for i in range(n)]
def MXI(): return [[LI()]for i in range(n)]
def SI(): return input().rstrip()
def printns(x): print('\n'.join(x))
def printni(x): print('\n'.join(list(map(str,x))))
inf = 10**17
mod = 10**9 + 7

x,y,z,k=MI()
A=sorted(LI(),reverse=True)
B=sorted(LI(),reverse=True)
C=sorted(LI(),reverse=True)
Q=[[(A[0]+B[0]+C[0])*(-1),0,0,0]]
heapify(Q)
#print(Q)
i=0
ans=[]
#print(heappop(Q))
al=[[[-1]*x for i in range(y)] for j in range(z)]
al[0][0][0]=0
while i<k:
    a,u,v,w=heappop(Q)
    ans.append(-a)
    if u+1<x and al[u+1][v][w]==-1:
        heappush(Q,[-A[u+1]-B[v]-C[w],u+1,v,w])
        al[u+1][v][w]=0
    if v+1<y and al[u][v+1][w]==-1:
        heappush(Q,[-A[u]-B[v+1]-C[w],u,v+1,w])
        al[u][v+1][w]=0
    if w+1<z and al[u][v][w+1]==-1:
        heappush(Q,[-A[u]-B[v]-C[w+1],u,v,w+1])
        al[u][v][w+1]=0
    i+=1
#print(len(ans))
for i in range(k):
    print(ans[i])

Submission status: Time Limit Exceeded

Solution code:
# coding: utf-8
# hello worldと表示する
#float型を許すな
#numpyはpythonで
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**7)
from collections import Counter, deque
from collections import defaultdict
from itertools import combinations, permutations, accumulate, groupby, product
from bisect import bisect_left,bisect_right
from heapq import heapify, heappop, heappush
from math import floor, ceil,pi,factorial
from operator import itemgetter
def I(): return int(input())
def MI(): return map(int, input().split())
def LI(): return list(map(int, input().split()))
def LI2(): return [int(input()) for i in range(n)]
def MXI(): return [[LI()]for i in range(n)]
def SI(): return input().rstrip()
def printns(x): print('\n'.join(x))
def printni(x): print('\n'.join(list(map(str,x))))
inf = 10**17
mod = 10**9 + 7

x,y,z,k=MI()
A=LI()
B=LI()
C=LI()
lis=[]
for i in range(x):
    for j in range(y):
        lis.append(A[i]+B[j])
lis.sort(reverse=True)
lisan=[]
for i in range(min(k,x*y)):
    for j in range(z):
        lisan.append(lis[i]+C[j])
lisan.sort(reverse=True)
for i in range(k):
    print(lisan[i])

Submission status: Time Limit Exceeded

Solution code:
import sys
input = sys.stdin.readline
def main():
  R=list()
  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()))
  for i in range(X):
    for j in range(Y):
      for k in range(Z):
        R.append(A[i]+B[j]+C[k])
  R=sorted(R,reverse=True)
  for i in range(K):
    print(R[i])
if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
R=list()
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()))
for i in range(X):
  for j in range(Y):
    for k in range(Z):
      R.append(A[i]+B[j]+C[k])
R=sorted(R,reverse=True)
for i in range(K):
  print(R[i])

Submission status: Time Limit Exceeded

Solution code:
import sys
input = sys.stdin.readline

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 = [0]*X*Y
i = 0
for a in A:
    for b in B:
        AB[i] = a + b
        i += 1
AB.sort(reverse=True)

ans = [0]*min(K, len(AB))*Z
i, j = 0, 0
for i in range(min(K, len(AB))):
    for c in C:
        ans[j] = AB[i] + c
        j += 1
ans.sort(reverse=True)

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

Submission status: Time Limit Exceeded

Solution code:
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 = [0]*X*Y
i = 0
for a in A:
    for b in B:
        AB[i] = a + b
        i += 1
AB.sort(reverse=True)

ans = [0]*min(K, len(AB))*Z
i, j = 0, 0
for i in range(min(K, len(AB))):
    for c in C:
        ans[j] = AB[i] + c
        j += 1
ans.sort(reverse=True)

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

Submission status: Time Limit Exceeded

Solution code:
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 = [0]*X*Y
i = 0
for a in A:
    for b in B:
        AB[i] = a + b
        i += 1
AB.sort(reverse=True)

ans = [0]*min(K, len(AB))*Z
i, j = 0, 0
for i in range(min(K, len(AB))):
    for c in C:
        ans[j] = AB[i] + c
        j += 1
ans.sort(reverse=True)

for i in range(min(K, len(AB)*Z)):
    print(ans[i])

Submission status: Time Limit Exceeded

Solution code:
# でつoO(YOU PLAY WITH THE CARDS YOU'RE DEALT..)
from heapq import heappop, heappush
import sys
def main(X, Y, Z, K, A, B, C):
    A.sort(reverse=True)
    B.sort(reverse=True)
    C.sort(reverse=True)
    used = [[[False] * Z for _ in range(Y)] for __ in range(X)]
    q = [(-(A[0] + B[0] + C[0]), 0, 0, 0)]
    used[0][0][0] = True
    for i in range(K):
        v, ai, bi, ci = heappop(q)
        print(-v)
        for nai, nbi, nci in [(ai + 1, bi, ci), (ai, bi + 1, ci), (ai, bi, ci + 1)]:
            if nai >= X or nbi >= Y or nci >= Z: continue
            if used[nai][nbi][nci]: continue
            used[nai][nbi][nci] = True
            heappush(q, (-(A[nai] + B[nbi] + C[nci]), nai, nbi, nci))

if __name__ == '__main__':
    input = sys.stdin.readline
    X, Y, Z, K = map(int, input().split())
    *A, = map(int, input().split())
    *B, = map(int, input().split())
    *C, = map(int, input().split())
    main(X, Y, Z, K, A, B, C)

Submission status: Time Limit Exceeded

Solution code:
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(reverse=True)
#print(AB)
AB = AB[:K]

ABC = []
for i in range(len(AB)):
    for j in range(Z):
        ABC.append(AB[i] + C[j])
        
ABC.sort(reverse=True)
ABC = ABC[:K]

for i in ABC:
    print(i)