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: Accepted

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=[]
heapq.heappush(hq,(-(A[0]+B[0]+C[0]),0,0,0))
searched={(0,0,0)}
a,b,c=0,0,0
D=((1,0,0),(0,1,0),(0,0,1))
for _ in range(k):
    abc,a,b,c=heapq.heappop(hq)
    print(-abc)
    for dx,dy,dz in D:
        if not (a+dx,b+dy,c+dz) in searched:
            if a+dx<x and b+dy<y and c+dz<z:
                heapq.heappush(hq,(-(A[a+dx]+B[b+dy]+C[c+dz]),a+dx,b+dy,c+dz))
                searched.add((a+dx,b+dy,c+dz))

Submission status: Accepted

Solution code:
import heapq

x, y, z, k = map(int, raw_input().split())
a = sorted(map(int, raw_input().split()))
b = sorted(map(int, raw_input().split()))
c = sorted(map(int, raw_input().split()))

q = []
memo = set()
def qpush(q, ai, bi, ci):
    if ai >= 0 and bi >= 0 and ci >= 0:
        t = (-(a[ai] + b[bi] + c[ci]), ai, bi, ci)
        if not t in memo:
            memo.add(t)
            heapq.heappush(q, t)

qpush(q, len(a) - 1, len(b) - 1, len(c) - 1)
for _ in range(k):
    s, ai, bi, ci = heapq.heappop(q)
    qpush(q, ai - 1, bi, ci)
    qpush(q, ai, bi - 1, ci)
    qpush(q, ai, bi, ci - 1)
    print -s

Submission status: Accepted

Solution code:
a,b,c,k = map(int,input().split())

aa = list(map(int,input().split()))
aa.sort(reverse = True)
bb = list(map(int,input().split()))
bb.sort(reverse = True)
cc = list(map(int,input().split()))
cc.sort(reverse = True)
al = []
aal = []
for i in aa:
    for j in bb:
        al.append(i+j)
al.sort()
if len(al) > k:
    al = al[len(al)-k:]

for i in al:
    for j in cc:
        aal.append(i+j)
aal.sort()

if len(aal) > k:
    aal = aal[len(aal)-k:]
aal.reverse()
for i in aal:
    print(i)

Submission status: Accepted

Solution code:
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)

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

temp = sorted(temp, reverse=True)
temp = temp[:K]

ans = []
for c in C:
	for num in temp:
		ans.append(num+c)

ans = sorted(ans, reverse=True)
for i in range(K):
	print(ans[i])

Submission status: Accepted

Solution code:
#!/usr/bin/env python
import numpy as np
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 = []
A.sort(reverse=True)
B.sort(reverse=True)
C.sort(reverse=True)
for i in range(min(K,X)):
    for j in range(min((K//(i+1),Y))):
        for k in range(min(((K//(i+1)+1)//(j+1)),Z)):
            D.append(A[i]+B[j]+C[k])
D.sort(reverse=True)
for i in range(K):
    print(int(D[i]))

Submission status: Accepted

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 = sorted(a)
b = sorted(b)
c = sorted(c)

la = []

for i in range(x):
    s = x-i
    for n in range(max(y-5-3000//s,0),y):
        u = y-n
        for m in range(max(z-5-3000//(s*u),0),z):
            #print(s,u,m)
            la.append(a[i]+b[n]+c[m])

la = sorted(la)

for i in range(k):
    print(la[-i-1])

Submission status: Accepted

Solution code:
import numpy as np
import bisect
from collections import deque

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()))

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

YZ = Y * Z

def createBitArray(X, Y, Z):
    size = X*Y*Z // 60 + 1
    return(np.zeros(size, 'int64'))

def getBit(R, a, b, c):
    pos = a * YZ + b * Z + c
    loc = pos // 60
    bit = 2 ** (pos % 60)
    return(R[loc] & bit)

def putBit(R, a, b, c):
    pos = a * YZ + b * Z + c
    loc = pos // 60
    bit = 2 ** (pos % 60)
    R[loc] = R[loc] | bit

R = createBitArray(X, Y, Z)

l = []
m = []

M = A[0] + B[0] + C[0]
position = bisect.bisect(l, M)
bisect.insort(l, M)
m.insert(position, (0, 0, 0))
putBit(R, 0, 0, 0)

for i in range(K):
    print(l[len(m)-1])

    a, b, c = m[len(m)-1]

    del l[len(m)-1]
    del m[len(m)-1]

    if a+1 < X and getBit(R, a+1, b, c) == 0:
        M = A[a+1] + B[b] + C[c]
        position = bisect.bisect(l, M)
        bisect.insort(l, M)
        m.insert(position, (a+1, b, c))
        putBit(R, a+1, b, c)

    if b+1 < Y and getBit(R, a, b+1, c) == 0:
        M = A[a] + B[b+1] + C[c]
        position = bisect.bisect(l, M)
        bisect.insort(l, M)
        m.insert(position, (a, b+1, c))
        putBit(R, a, b+1, c)

    if c+1 < Z and getBit(R, a, b, c+1) == 0:
        M = A[a] + B[b] + C[c+1]
        position = bisect.bisect(l, M)
        bisect.insort(l, M)
        m.insert(position, (a, b, c+1))
        putBit(R, a, b, c+1)

Submission status: Accepted

Solution code:
X, Y, Z, K= map(int,input().split())
A=list(map(int,input().split()))
A.sort(reverse=True)
B=list(map(int,input().split()))
B.sort(reverse=True)
C=list(map(int,input().split()))
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 range(K):
    print(ABC[i])

Submission status: Accepted

Solution code:
ri = lambda: int(input())
rl = lambda: list(map(int,input().split()))
rr = lambda N: [ri() for _ in range(N)]
YN = lambda b: print('YES') if b else print('NO')
yn = lambda b: print('Yes') if b else print('No')
OE = lambda x: print('Odd') if x%2 else print('Even')
INF = 10**18

X,Y,Z,K=rl()
A=rl()
B=rl()
C=rl()
A.sort(reverse=True)
B.sort(reverse=True)
C.sort(reverse=True)
ans = []
for a in range(1,X+1):
    for b in range(1,Y+1):
        for c in range(1,Z+1):
            if a*b*c<=K:
                ans.append(A[a-1]+B[b-1]+C[c-1])
            else:
                break
ans.sort(reverse=True)
for i in range(K):
    print(ans[i])

Submission status: Accepted

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

#input
import numpy as np
[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()))

D = []
A.sort(reverse=True)
B.sort(reverse=True)
C.sort(reverse=True)

#make list
for i in range(min(K,X)):
    for j in range(min((K//(i+1))+1,Y)):
        for k in range(min(((K//(i+1))+1)//(j+1),Z)):
                D.append(A[i]+B[j]+C[k])
D.sort(reverse=True)
for i in range(K):
    print(int(D[i]))

Submission status: Accepted

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_total_list = []
total_list = []

A.sort()
A.reverse()
if len(A) > K:
    A = A[0:K+1]

B.sort()
B.reverse()
if len(B) > K:
    B = B[0:K+1]

C.sort()
C.reverse()
if len(C) > K:
    C = C[0:K+1]

ab_total_list = []
for i in A:
    for j in B:
        ab_total_list.append(i+j)

ab_total_list.sort()
ab_total_list.reverse()
if len(ab_total_list) > K:
    ab_total_list = ab_total_list[0:K+1]

for i in range(0, K):
    for j in range(0, int(K/(i+1))):
        if j >= len(C) or i >= len(ab_total_list):
            break
        total = ab_total_list[i] + C[j]
        total_list.append(total)
        if (i*j) > K:
            break

total_list.sort()
total_list.reverse()
for i in range(0, K):
    print(total_list[i])

Submission status: Accepted

Solution code:
import heapq

x, y, z, k = map(int, raw_input().split())
a = sorted(map(int, raw_input().split()))
b = sorted(map(int, raw_input().split()))
c = sorted(map(int, raw_input().split()))

q = []
memo = set()
def qpush(q, ai, bi, ci):
    t = (-(a[ai] + b[bi] + c[ci]), ai, bi, ci)
    if not t in memo:
        memo.add(t)
        heapq.heappush(q, t)

qpush(q, len(a) - 1, len(b) - 1, len(c) - 1)
for _ in range(k):
    s, ai, bi, ci = heapq.heappop(q)
    if ai > 0:
        qpush(q, ai - 1, bi, ci)
    if bi > 0:
        qpush(q, ai, bi - 1, ci)
    if ci > 0:
        qpush(q, ai, bi, ci - 1)
    print -s

Submission status: Accepted

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


d = [e1+e2 for e1 in a for e2 in b]
d.sort(reverse=True)
d = d[:k]

e = [e1+e2 for e1 in d for e2 in c]
e.sort(reverse=True)


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

Submission status: Accepted

Solution code:
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.sort(reverse=True)
b.sort(reverse=True)
c.sort(reverse=True)
if k>x: a=a[:k]
if k>y: b=b[:k]
if k>z: c=c[:k]
d=[]
ans=[]
for i in a:
    for j in b:
        d.append(i+j)
d.sort(reverse=True)
if len(d)>k: d=d[:k]
for i in c:
    for j in d:
        ans.append(i+j)
ans.sort(reverse=True)
for i in range(k):
    print(ans[i])

Submission status: Accepted

Solution code:
# D
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 index_i, i in enumerate(a):
    for index_j, j in enumerate(b):
        for index_l, l in enumerate(c):
            if ((index_i+1)*(index_j+1)*(index_l+1) <= k):
                ans.append(i+j+l)
            else:
                break
ans.sort(reverse=True)
for i in range(k):
    print(ans[i])

Submission status: Accepted

Solution code:
x, y, z, kk = 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)

p = []
for i in range(x):
    for j in range(y):
        for k in range(z):
            if (i + 1) * (j + 1) * (k + 1) <= kk:
                p.append(a[i] + b[j] + c[k])
            else:
                break
p.sort(reverse=True)
for i in range(kk):
    print(p[i])

Submission status: Accepted

Solution code:

def main():
    x,y,z,k = [int(i) for i in 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.sort(reverse=True)
    b.sort(reverse=True)
    c.sort(reverse=True)

    ans = []

    for i in range(x):
        if i > k:
            break
        for j in range(y):
            if i * j > k:
                break
            for m in range(z):
                if i * j * m > k:
                    break
                ans.append(a[i]+b[j]+c[m])

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


main()

Submission status: Accepted

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)
k=min(K,X*Y)
AB=AB[:k]
ABC=[]
for i in range(k):
    for j in range(Z):
        ABC.append(AB[i]+C[j])
ABC.sort(reverse=True)
for i in range(K):
    print(ABC[i])

Submission status: Accepted

Solution code:
import heapq
X,Y,Z,K=map(int,input().split())
A=sorted([-int(i) for i in input().split()])
B=sorted([-int(i) for i in input().split()])
C=sorted([-int(i) for i in input().split()])
q=[]
heapq.heappush(q,(A[0]+B[0]+C[0],0,0,0))
S={(0,0,0)}
for n in range(K):
    p,i,j,k=heapq.heappop(q)
    if i+1<X and not((i+1,j,k) in S):
        S.add((i+1,j,k))
        heapq.heappush(q,(A[i+1]+B[j]+C[k],i+1,j,k))
    if j+1<Y and not((i,j+1,k) in S):
        S.add((i,j+1,k))
        heapq.heappush(q,(A[i]+B[j+1]+C[k],i,j+1,k))
    if k+1<Z and not((i,j,k+1) in S):
        S.add((i,j,k+1))
        heapq.heappush(q,(A[i]+B[j]+C[k+1],i,j,k+1))
    print(-p)

Submission status: Accepted

Solution code:
x, y, z, k = [int(x) for x in input().split()]
a = [int(x) for x in input().split()]
b = [int(x) for x in input().split()]
c = [int(x) for x in input().split()]

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

d = [e1+e2 for e1 in a for e2 in b]
d.sort(reverse=True)
d = d[:k]

e = [e1+e2 for e1 in d for e2 in c]    
e.sort(reverse=True)

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

Submission status: Accepted

Solution code:
from heapq import heappop, heappush

X, Y, Z, K = [int(s) for s in input().split()]
A = [int(s) for s in input().split()]
B = [int(s) for s in input().split()]
C = [int(s) for s in input().split()]
A.sort(reverse=True)
B.sort(reverse=True)
C.sort(reverse=True)
counted = set()
h = [(-(A[0] + B[0] + C[0]), 0, 0, 0)]
for _ in range(K):
    s, i, j, k = heappop(h)
    print(-s)
    if X > i+1 and (i+1, j, k) not in counted:
        heappush(h, (-(A[i+1] + B[j] + C[k]), i+1, j, k))
        counted.add((i+1, j, k))
    if Y > j+1 and (i, j+1, k) not in counted:
        heappush(h, (-(A[i] + B[j+1] + C[k]), i, j+1, k))
        counted.add((i, j+1, k))
    if Z > k+1 and (i, j, k+1) not in counted:
        heappush(h, (-(A[i] + B[j] + C[k+1]), i, j, k+1))
        counted.add((i, j, k+1))

Submission status: Accepted

Solution code:
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)


AB = []
for i in range(X):
    for j in range(Y):
        AB.append(A[i] + B[j])
AB.sort(reverse=True)
AB = AB[:K]

ans = []
for ab in AB:
    for c in C:
        ans.append(ab + c)
        
ans.sort(reverse=True)
print(*ans[:K], sep='\n')

Submission status: Accepted

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 = sorted(A,reverse=True)[:k]
B = sorted(B,reverse=True)[:k]
C = sorted(C,reverse=True)[:k]

list_ans = []
for index_a,a in enumerate(A):
  for index_b,b in enumerate(B):
    for index_c,c in enumerate(C):
      if (index_a + 1) * (index_b + 1) * (index_c + 1) > k:
        break
      list_ans.append(a+b+c)


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

Submission status: Accepted

Solution code:
X, Y, Z, K = map(int, input().split())
A = [int(_) for _ in input().split()]
B = [int(_) for _ in input().split()]
C = [int(_) for _ in input().split()]
A = sorted(A)[::-1]
B = sorted(B)[::-1]
C = sorted(C)[::-1]

List = []

for i in range(X):
    for j in range(Y):
        for k in range(Z):
            if (i+1)*(j+1)*(k+1) > K:
                break
            else:
                List.append(A[i]+B[j]+C[k])

List = sorted(List)[-1:-K-1:-1]
for i in range(K):
    print(List[i])

Submission status: Accepted

Solution code:
x, y, z, k = [int(x) for x in input().split()]
a = [int(x) for x in input().split()]
b = [int(x) for x in input().split()]
c = [int(x) for x in input().split()]
a.sort(reverse=True)
b.sort(reverse=True)
c.sort(reverse=True)

d = [e1+e2 for e1 in a for e2 in b]
d.sort(reverse=True)
d = d[:k]

e = [e1+e2 for e1 in d for e2 in c]
e.sort(reverse=True)

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

Submission status: Accepted

Solution code:

import heapq
import sys
stdin = sys.stdin
 
sys.setrecursionlimit(10**5) 
def li(): return map(int, stdin.readline().split())
i_a, i_b, i_c, K = tuple(li())
A = list(li())
B = list(li())
C = list(li())
A.sort()
B.sort()
C.sort()

memo = {}
heap = []
def val(a,b,c):
    if a<0 or b<0 or c<0:
        return False
    return A[a] + B[b] + C[c]
total = val(i_a-1, i_b-1, i_c-1)
heap = [(-total, i_a-1, i_b-1, i_c-1)]
while K > 0:
    K -= 1
    cur = heapq.heappop(heap)
    print(-cur[0])
    a,b,c = cur[1], cur[2], cur[3]
    if (a-1, b,c) not in memo:
        va = val(a-1,b,c)
        if va:
            memo[(a-1,b,c)] = True
            heapq.heappush(heap, [-va, a-1, b, c])
    if (a, b-1,c) not in memo:
        vb = val(a,b-1,c)
        if vb:
            memo[(a,b-1,c)] = True
            heapq.heappush(heap, [-vb, a, b-1, c])

    if (a, b,c-1) not in memo:
        vc = val(a,b,c-1)
        if vc:
            memo[(a,b,c-1)] = True
            heapq.heappush(heap, [-vc, a, b, c-1])

Submission status: Accepted

Solution code:
x,y,z,k=map(int,input().split())
a=list(map(int,input().split()))
a.sort(reverse=True)
b=list(map(int,input().split()))
b.sort(reverse=True)
c=list(map(int,input().split()))
c.sort(reverse=True)
d=[i+j for i in a for j in b]
d.sort(reverse=True)
e=[i+j for i in c for j in d[:k]]
e.sort(reverse=True)
for i in range(k):
    print(e[i])

Submission status: Accepted

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)
t = []

for i in range(x):
    for j in range(y):
        for r in range(z):
            if (i+1)*(j+1)*(r+1) > k:
                break
            else:
                t.append(a[i]+b[j]+c[r])

t.sort(reverse = True)

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

Submission status: Accepted

Solution code:
x, y, z, k = map(int, input().split())
a = [int(m) for m in input().split()]
b = [int(m) for m in input().split()]
c = [int(m) for m in input().split()]
a.sort(reverse=True)
b.sort(reverse=True)
c.sort(reverse=True)
s = []
for i in range(x):
    for j in range(y):
        s.append(a[i] + b[j])

s.sort(reverse=True)
s1 = []
for i in range(min(x * y, k)):
    s1.append(s[i])

t = []
for i in range(min(x * y, k)):
    for j in range(z):
        t.append(s1[i] + c[j])

t.sort(reverse=True)

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

Submission status: Accepted

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 = sorted(a)[::-1]
b = sorted(b)[::-1]
c = sorted(c)[::-1]
l = []
for i in range(x):
    for j in range(y):
        for m in range(z):
            if (i+1)*(j+1)*(m*1)>k:
                break
            l.append(a[i]+b[j]+c[m])
l = sorted(l)[::-1]
for i in range(k):
    print(l[i])

Submission status: Accepted

Solution code:
x, y, z, k = map(int, input().split())
m = []
for _ in range(3):
    m.append(sorted(list(map(int, input().split())), reverse=True))
 
def sorted_sum(list_a, list_b):
    s = []
    for x in list_a:
        for y in list_b:
            s.append(x + y)
    return sorted(s, reverse=True)
 
ans = sorted_sum(sorted_sum(m[0], m[1])[0:k], m[2])[0:k]
for i in range(0, k):
    print(ans[i])

Submission status: Accepted

Solution code:
# https://atcoder.jp/contests/abc123/tasks/abc123_d

import itertools
import collections
import bisect

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)

    # big value
    INF = int(1e15)
    x = 0
    y = 0
    AB = []
    for a in A:
        for b in B:
            AB.append(a + b)

    AB.sort(reverse=True)
    AB = AB[:K]
    # print(A)
    # print(B)
    # print(AB)

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

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


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
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()))

d = []

for e1 in a:
  for e2 in b:
    d.append(e1+e2)

d.sort(reverse=True)
d = d[:k]
e = []

for e1 in d:
  for e2 in c:
    e.append(e1+e2)
    
e.sort(reverse=True)

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

Submission status: Accepted

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


memo = {}
i = j = k = 0

h = []
heapq.heappush(h, (-(a[i]+b[j]+c[k]), i,j,k))
for _ in range(K):
    cost, i, j, k = heapq.heappop(h)
    print(-cost)
    for dx, dy, dz in ((1,0,0), (0,1,0), (0,0,1)):
        if (i+dx, j+dy, k+dz) in memo:
            continue
        if i+dx<x and j+dy<y and k+dz<z:
            heapq.heappush(h, (-(a[i+dx]+b[j+dy]+c[k+dz]), i+dx, j+dy, k+dz))
            memo[(i+dx,j+dy,k+dz)] = 1

Submission status: Accepted

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)

kouho = set()
done = set()


def f(t):
    x, y, z = t
    if x >= X or y >= Y or z >= Z:
        return 0
    return A[x] + B[y] + C[z]


def main():
    start = (f((0, 0, 0)), (0, 0, 0))
    kouho.add(start)
    done.add(start)

    for k in range(K):
        d = max(kouho)
        kouho.remove(d)

        x, y, z = d[1]
        toadd = [(x, y, z+1), (x, y+1, z), (x+1, y, z)]
        for ta in toadd:
            t = (f(ta), ta)
            if t in done:
                continue
            kouho.add(t)
            done.add(t)

        print(d[0])


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
X,Y,Z,K=map(int, raw_input().split())
A=map(int, raw_input().split())
B=map(int, raw_input().split())
C=map(int, raw_input().split())

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

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

L2=[]
for ab in L:
	for c in C:
		L2.append(ab+c)

L2.sort(reverse=True)

for i in range(K):
	print L2[i]

Submission status: Accepted

Solution code:
x, y, z, k = map(int, input().split())
m = []
for _ in range(3):
    m.append(sorted(list(map(int, input().split())), reverse=True))

def sorted_sum(list_a, list_b, limit):
    s = []
    for x in list_a:
        for y in list_b:
            s.append(x + y)
    return sorted(s, reverse=True)[0:limit]


def consume_diff(s, a_val, list_b, b_index):
    diff = a_val - list_b[b_index]
    for i in range(b_index + 1, len(list_b)):
        if list_b[b_index] - list_b[i] > diff:
            break
        s.append(a_val + list_b[i])



ans = sorted_sum(sorted_sum(m[0], m[1], k), m[2], k)
for i in range(min([k, len(ans)])):
    print(ans[i])

Submission status: Accepted

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

Submission status: Accepted

Solution code:
#!usr/bin/env python3
from collections import defaultdict
from collections import deque
from heapq import heappush, heappop
import sys
import math
import bisect
import random
import itertools
sys.setrecursionlimit(10**5)
stdin = sys.stdin
def LI(): return list(map(int, stdin.readline().split()))
def LF(): return list(map(float, stdin.readline().split()))
def LI_(): return list(map(lambda x: int(x)-1, stdin.readline().split()))
def II(): return int(stdin.readline())
def IF(): return float(stdin.readline())
def LS(): return list(map(list, stdin.readline().split()))
def S(): return list(stdin.readline().rstrip())
def IR(n): return [II() for _ in range(n)]
def LIR(n): return [LI() for _ in range(n)]
def FR(n): return [IF() for _ in range(n)]
def LFR(n): return [LI() for _ in range(n)]
def LIR_(n): return [LI_() for _ in range(n)]
def SR(n): return [S() for _ in range(n)]
def LSR(n): return [LS() for _ in range(n)]
mod = 1000000007
inf = float('INF')

#A
def A():
    a = IR(5)
    k = II()
    if max(a) - min(a) > k:
        print(":(")
    else:
        print("Yay!")
    return

#B
def B():
    a = IR(5)
    b = a[0]
    ans = 0
    for a_ in a:
        if a_ % 10 != 0:
            if b % 10> a_ % 10:
                b = a_
    flg = 0
    for a_ in a:
        if a_ != b or flg:
            ans += math.ceil(a_ / 10) * 10
        else:
            ans += b
            flg = 1
    print(ans)
            
    
    return

#C
def C():
    n = II()
    ai = IR(5)
    print(math.ceil(n / min(ai)) + 4)
        
        
    return

#D
def D():
    x, y, z, K = LI()
    a = LI()
    a.sort(reverse=True)
    b = LI()
    b.sort(reverse = True)
    c = LI()
    c.sort(reverse=True)
    ab = []
    for a_ in a:
        for b_ in b:
            ab.append(a_ + b_)
    ab.sort(reverse = True)
    ab = ab[:min(x * y, K)]
    ans = []
    for ab_ in ab:
        for c_ in c:
            ans.append(ab_ + c_)
    ans.sort(reverse = True)
    for k in range(K):
        print(ans[k])



        
                    

    return

#E
def E():
    return

#F
def F():
    return

#G
def G():
    return

#H
def H():
    return

#Solve
if __name__ == '__main__':
    D()

Submission status: Accepted

Solution code:
from heapq import heappush, heappop


def solve(X, Y, Z, K, As, Bs, Cs):
    As.sort()
    Bs.sort()
    Cs.sort()
    ADs = [a2 - a1 for a1, a2 in zip(As, As[1:])][::-1]
    BDs = [a2 - a1 for a1, a2 in zip(Bs, Bs[1:])][::-1]
    CDs = [a2 - a1 for a1, a2 in zip(Cs, Cs[1:])][::-1]

    m = As[-1] + Bs[-1] + Cs[-1]
    h = []
    ans = [m]
    if ADs:
        heappush(h, (ADs[0], (0, -1, -1)))
    if BDs:
        heappush(h, (BDs[0], (-1, 0, -1)))
    if CDs:
        heappush(h, (CDs[0], (-1, -1, 0)))
    taken = set()

    for i in range(K - 1):
        p, stacks = heappop(h)
        while (p, stacks) in taken:
            p, stacks = heappop(h)
        taken.add((p, stacks))
        ans.append(m - p)

        if stacks[0] + 1 < len(ADs):
            heappush(h, ((p + ADs[stacks[0] + 1]), (stacks[0] + 1, stacks[1], stacks[2])))
        if stacks[1] + 1 < len(BDs):
            heappush(h, ((p + BDs[stacks[1] + 1]), (stacks[0], stacks[1] + 1, stacks[2])))
        if stacks[2] + 1 < len(CDs):
            heappush(h, ((p + CDs[stacks[2] + 1]), (stacks[0], stacks[1], stacks[2] + 1)))

    return "\n".join([str(a) for a in ans])

if __name__ == "__main__":
    X, Y, Z, K = tuple(map(int, input().split(" ")))
    As = list(map(int, input().split(" ")))
    Bs = list(map(int, input().split(" ")))
    Cs = list(map(int, input().split(" ")))
    print(solve(X, Y, Z, K, As, Bs, Cs))

Submission status: Accepted

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()))
C.sort(reverse=True)
E=[]
ans=[]
for i in range(X):
    for j in range(Y):
        E.append(A[i]+B[j])
E.sort(reverse=True)
for i in range(min(K,len(E))):
    for j in range(min(K,Y)):
        ans.append(E[i]+C[j])
ans.sort(reverse=True)
for i in range(K):
    print(ans[i])

Submission status: Accepted

Solution code:


def main():
    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()))
    A.sort(reverse=True)
    B.sort(reverse=True)
    C.sort(reverse=True)


    data = []
    for i in range(X):
        for j in range(Y):
            if i * j > K:
                break
            for k in range(Z):
                if i * j * k > K:
                    break
                data.append(A[i] + B[j] + C[k])

    data.sort(reverse=True)

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

if __name__ == '__main__':
    main()

Submission status: Accepted

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)

s = [0] * (len(a) * len(b))
ans = [0] * (3000 * len(c))

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

i = 0
for S in s[:3000]:
    for C in c:
        ans[i] = C + S
        i += 1
ans.sort(reverse=True)

for i in ans[:k]:
    print(i)

Submission status: Accepted

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)
tot = []
for i in range(X):
   for j in range(Y):
      for k in range(Z):
         if((i+1)*(j+1)*(k+1) <= K): tot.append(a[i] + b[j] + c[k])
         else: break
tot.sort(reverse = True)
for i in range(K):print(tot[i])