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:
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)
xl = set(range(x))
yl = set(range(y))
zl = set(range(z))
t = []
for i in xl:
    for j in yl:
        for l in zl:
            if (i+1) * (j+1) * (l+1) <= k:
                t.append(a[i]+b[j]+c[l])
            else:
                break
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.sort(reverse=True)
b.sort(reverse=True)
c.sort(reverse=True)
t = []
for i in range(x):
    for j in range(y):
        for l in range(z):
            if (i+1) * (j+1) * (l+1) <= k:
                t.append(a[i]+b[j]+c[l])
            else:
                break
t.sort(reverse=True)
for i in range(k):
    print(t[i])

Submission status: Accepted

Solution code:
import sys; sys.setrecursionlimit(50000)
input = sys.stdin.readline

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

result = []
for x in range(X):
    for y in range(Y):
        if x * y > K: break
        for z in range(Z):
            if x * y * z > K: break
            result.append(A[x]+B[y]+C[z])
            
for i in sorted(result, reverse=True)[:K]:
    print(i)

Submission status: Accepted

Solution code:
import sys; sys.setrecursionlimit(50000)
input = sys.stdin.readline

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

result = []
for x in range(X):
    for y in range(Y):
        if x * y > K: break
        for z in range(Z):
            if x * y * z > K: break
            result.append(A[x]+B[y]+C[z])
result.sort(reverse=True)
for i in range(K):
    print(result[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)
ans=[]
for i in range(x):
  for j in range(y):
    for k in range(z):
      if (i+1)*(j+1)*(k+1)<=K:
        ans.append(a[i]+b[j]+c[k])
      else:
        break
ans.sort(reverse=True)
for i in range(K):
  print(ans[i])

Submission status: Accepted

Solution code:
import itertools
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 = [A,B,C]
if X*Y*Z <= 3000:
  M = list(itertools.product(*L))
  T = []
  for i in range(len(M)):
    T.append(sum(M[i]))
  T.sort()
  for i in range(len(T)-1,len(T)-K-1,-1):
    print(T[i])
else:
  T = []
  for i in range(X):
    for j in range(Y):
      T.append(A[i]+B[j])
  T.sort()
  T.reverse()
  U = []
  for i in range(K):
    U.append(T[i])
  V = []
  for i in range(K):
    for j in range(Z):
      V.append(U[i]+C[j])
  V.sort()
  V.reverse()
  for i in range(K):
    print(V[i])

Submission status: Accepted

Solution code:
# solution 3
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)
Q = []
s = []
heapq.heappush(Q, (-A[0]-B[0]-C[0], 0, 0, 0))
for n in range(K):
    q, i, j, k = heapq.heappop(Q)
    print(-q)
    if i < X-1 and (i+1, j, k) not in s:
            heapq.heappush(Q, (- A[i+1] - B[j] - C[k], i+1, j, k))
            s.append((i + 1, j, k))
    if j < Y-1 and (i, j+1, k) not in s:
            heapq.heappush(Q, (- A[i] - B[j+1] - C[k], i, j+1, k))
            s.append((i, j + 1, k))
    if k < Z-1 and (i, j, k+1) not in s:
            heapq.heappush(Q, (- A[i] - B[j] - C[k+1], i, j, k+1))
            s.append((i, j, k + 1))

Submission status: Accepted

Solution code:
# solution 3
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)
Q = []
s = set()
heapq.heappush(Q, (-A[0]-B[0]-C[0], 0, 0, 0))
for n in range(K):
    q, i, j, k = heapq.heappop(Q)
    print(-q)
    if i < X-1 and (i+1, j, k) not in s:
            heapq.heappush(Q, (- A[i+1] - B[j] - C[k], i+1, j, k))
            s.add((i + 1, j, k))
    if j < Y-1 and (i, j+1, k) not in s:
            heapq.heappush(Q, (- A[i] - B[j+1] - C[k], i, j+1, k))
            s.add((i, j + 1, k))
    if k < Z-1 and (i, j, k+1) not in s:
            heapq.heappush(Q, (- A[i] - B[j] - C[k+1], i, j, k+1))
            s.add((i, j, k + 1))

Submission status: Accepted

Solution code:
import sys; sys.setrecursionlimit(50000)
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()))
A.sort(reverse=True)
B.sort(reverse=True)
C.sort(reverse=True)

result = []
for x in range(X):
    for y in range(Y):
        if x * y > K: break
        for z in range(Z):
            if x * y * z > K: break
            result.append(A[x]+B[y]+C[z])
result.sort(reverse=True)
for i in range(K):
    print(result[i])

Submission status: Accepted

Solution code:
# solution 3
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)
Q = []
s = []
heapq.heappush(Q, (-A[0]-B[0]-C[0], 0, 0, 0))
for n in range(K):
    q, i, j, k = heapq.heappop(Q)
    print(-q)
    if i < X-1 and [i+1, j, k] not in s:
            heapq.heappush(Q, (- A[i+1] - B[j] - C[k], i+1, j, k))
            s.append([i + 1, j, k])
    if j < Y-1 and [i, j+1, k] not in s:
            heapq.heappush(Q, (- A[i] - B[j+1] - C[k], i, j+1, k))
            s.append([i, j + 1, k])
    if k < Z-1 and [i, j, k+1] not in s:
            heapq.heappush(Q, (- A[i] - B[j] - C[k+1], i, j, k+1))
            s.append([i, j, k + 1])

Submission status: Accepted

Solution code:
# solution 3
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)
Q = []
s = []
heapq.heappush(Q, (-A[0]-B[0]-C[0], 0, 0, 0))
for n in range(K):
    q, i, j, k = heapq.heappop(Q)
    print(-q)
    if i < X-1:
        if [i+1, j, k] not in s:
            heapq.heappush(Q, (- A[i+1] - B[j] - C[k], i+1, j, k))
            s.append([i + 1, j, k])
    if j < Y-1:
        if [i, j+1, k] not in s:
            heapq.heappush(Q, (- A[i] - B[j+1] - C[k], i, j+1, k))
            s.append([i, j + 1, k])
    if k < Z-1:
        if [i, j, k+1] not in s:
            heapq.heappush(Q, (- A[i] - B[j] - C[k+1], i, j, k+1))
            s.append([i, j, k + 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)

# まずA, Bで総当たり、上位K個をスタック
tmp = [a+b for a in A for b in B]
tmp.sort(reverse=True)
tmp = tmp[:K]

# 残りのc個に対しても総当たり
ans = [t+c for t in tmp for c in C]
ans.sort(reverse=True)
ans = ans[:K]
for s in ans:
    print(s)

Submission status: Accepted

Solution code:
from collections import defaultdict
import heapq
inpl = lambda: list(map(int,input().split()))

X, Y, Z, K = inpl()
A = [ sorted(inpl(), reverse=True) for _ in range(3) ]
N = [X, Y, Z]

mem = defaultdict(int)
score = sum([A[i][0] for i in range(3)])
mem[(0,0,0)] = 1
candidates = []
heapq.heappush(candidates, (-score,(0,0,0)))

for i in range(K):
    c = heapq.heappop(candidates)
    print(-c[0])
    n = list(c[1])
    
    for p in range(3):
        if n[p] < N[p]-1:
            n[p] += 1
            if mem[tuple(n)] == 0:
                mem[tuple(n)] = 1
                score = sum([A[j][n[j]] for j in range(3)])
                heapq.heappush(candidates, (-score,tuple(n)))
            n[p] -= 1

Submission status: Accepted

Solution code:
# solution 2
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)
L = []
for i in range(X):
    for j in range(Y):
        if (i+1)*(j+1) > K:
            break
        for k in range(Z):
            if (i+1)*(j+1)*(k+1) > K:
                break
            else:
                L.append(A[i] + B[j] + C[k])
L.sort(reverse=True)
for l in range(K):
    print(L[l])

Submission status: Accepted

Solution code:
import heapq

X, Y, Z, K = map(int, input().split())
a_list = list(map(int, input().split()))
b_list = list(map(int, input().split()))
c_list = list(map(int, input().split()))

a_list.sort(reverse = True)
b_list.sort(reverse = True)
c_list.sort(reverse = True)

heap = []
heapq.heappush(heap, (-(a_list[0] + b_list[0] + c_list[0]), 0, 0, 0))
searched = []
result = [0] * K

for k in range(K):
    elem = heapq.heappop(heap)
    result[k] = - elem[0]

    if elem[1] + 1 <= X - 1:
        a_next = (-(a_list[elem[1] + 1] + b_list[elem[2]] + c_list[elem[3]]), elem[1] + 1, elem[2], elem[3])
        if not a_next in searched:
            heapq.heappush(heap, a_next)
            searched.append(a_next)

    if elem[2] + 1 <= Y - 1:
        b_next = (-(a_list[elem[1]] + b_list[elem[2] + 1] + c_list[elem[3]]), elem[1], elem[2] + 1, elem[3])
        if not b_next in searched:
            heapq.heappush(heap, b_next)
            searched.append(b_next)

    if elem[3] + 1 <= Z - 1:
        c_next = (-(a_list[elem[1]] + b_list[elem[2]] + c_list[elem[3] + 1]), elem[1], elem[2], elem[3] + 1)
        if not c_next in searched:
            heapq.heappush(heap, c_next)
            searched.append(c_next)

[print(k) for k in result]

Submission status: Accepted

Solution code:
from heapq import nlargest

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()
B.sort()

E = nlargest(K, [a+b for a in A for b in B])
F = nlargest(K, [e+c for e in E for c in C])
#print(F)
print("\n".join(map(str,F)))

Submission status: Accepted

Solution code:
# solution 2
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)
L = []
for i in range(X):
    for j in range(Y):
        for k in range(Z):
            if (i+1)*(j+1)*(k+1) <= K:
                L.append(A[i]+B[j]+C[k])
            else:
                break
L.sort(reverse=True)
for l in range(K):
    print(L[l])

Submission status: Accepted

Solution code:
import heapq
x, y, z, k = map(int, input().split())
X = [int(i) for i in input().split()]
Y = [int(i) for i in input().split()]
Z = [int(i) for i in input().split()]
X.sort(reverse=1)
Y.sort(reverse=1)
Z.sort(reverse=1)

Q = []
s = set()
heapq.heappush(Q, (-(X[0]+Y[0]+Z[0]), 0, 0, 0))

def push(i, j, l):
    if (i,j,l) not in s and i<x and j<y and l<y:
        heapq.heappush(Q, (-(X[i]+Y[j]+Z[l]), i, j, l))
        s.add((i, j, l))

for _ in range(k):
    answer, a, b, c = heapq.heappop(Q)
    print(-answer)
    push(a+1, b, c)
    push(a, b+1, c)
    push(a, b, c+1)

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)
abc = []

for i in range(x):
  
  for j in range(y):
   
    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=True)
abc = abc[0:k]
for i in abc:
  print(i)

Submission status: Accepted

Solution code:
import heapq
import sys
from itertools import product
X, Y, Z, K = [int(i) for i in sys.stdin.readline().split()]
A_ls = [int(i) for i in sys.stdin.readline().split()]
B_ls = [int(i) for i in sys.stdin.readline().split()]
C_ls = [int(i) for i in sys.stdin.readline().split()]
A_ls.sort(reverse=True)
B_ls.sort(reverse=True)
C_ls.sort(reverse=True)
_sum_ls = [(-(A_ls[0] + B_ls[0] + C_ls[0]), 0, 0, 0)]
heapq.heapify(_sum_ls)
for i in range(K):
    score, a, b, c = heapq.heappop(_sum_ls)
    print(- score)
    if len(A_ls) > a+1:
        cand = (- (A_ls[a+1] + B_ls[b] + C_ls[c]), a+1, b, c)
        if not cand in _sum_ls:
            heapq.heappush(_sum_ls, cand)
    if len(B_ls) > b+1:
        cand = (- (A_ls[a] + B_ls[b+ 1] + C_ls[c]), a, b+1, c)
        if not cand in _sum_ls:
            heapq.heappush(_sum_ls, cand)
    if len(C_ls) > c+1:
        cand = (- (A_ls[a] + B_ls[b] + C_ls[c+1]), a, b, c+1)
        if not cand in _sum_ls:
            heapq.heappush(_sum_ls, cand)

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)
Q = []
heapq.heappush(Q, (-A[0]-B[0]-C[0], 0, 0, 0))
for n in range(K):
    ans = heapq.heappop(Q)
    print(-ans[0])
    i, j, k = ans[1], ans[2], ans[3]
    if i < X-1:
        if (- A[i+1] - B[j] - C[k], i+1, j, k) not in Q:
            heapq.heappush(Q, (- A[i+1] - B[j] - C[k], i+1, j, k))
    if j < Y-1:
        if (- A[i] - B[j+1] - C[k], i, j+1, k) not in Q:
            heapq.heappush(Q, (- A[i] - B[j+1] - C[k], i, j+1, k))
    if k < Z-1:
        if (- A[i] - B[j] - C[k+1], i, j, k+1) not in Q:
            heapq.heappush(Q, (- A[i] - B[j] - C[k+1], i, j, k+1))

Submission status: Accepted

Solution code:
x, y, z, k = map(int, input().split())
X = [int(i) for i in input().split()]
Y = [int(i) for i in input().split()]
Z = [int(i) for i in input().split()]
X.sort(reverse=1)
Y.sort(reverse=1)
Z.sort(reverse=1)

answer = [i+j for i in X[:k] for j in Y[:k]]
answer.sort(reverse=1)

answer2 = [i+j for i in Z[:k] for j in answer[:k]]
answer2.sort(reverse=1)

for p in answer2[:k]:
    print(p)

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)

e = [i + j for i in a[:k] for j in b[:k]]
e.sort(reverse=True)
e = e[:k]
ans = [i + j for i in e for j in c[:k]]
ans.sort(reverse=True)

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

Submission status: Accepted

Solution code:
from heapq import heappush, heapreplace
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()))
    heap = []
    for i in b:
        for j in c:
            if len(heap) < k:
                heappush(heap, i+j)
            elif heap[0] < i+j:
                heapreplace(heap, i+j)
    ans = []            
    for i in heap:
        for j in a:
            if len(ans) < k:
                heappush(ans, i+j)
            elif ans[0] < i+j:
                heapreplace(ans, i+j)
    ans.sort()
    for val in reversed(ans):
        print(val)    
    return
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(key=lambda x:-x)
b.sort(key=lambda x:-x)
c.sort(key=lambda x:-x)
beauty=[]
index=0
for i in range(x):
    for j in range(y):
        for l in range(z):
            if (i+1)*(j+1)*(l+1)<=k:
                beauty.append(a[i]+b[j]+c[l])
            else:
                break
beauty.sort(key=lambda x:-x)
for i in range(k):
    print(beauty[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)


scores = []
for a in range(len(A)):
    for b in range(len(B)):
        if (a + 1) * (b + 1) > K:
            break
        for c in range(len(C)):
            if (a + 1) * (b + 1) * (c + 1) > K:
                break
            score = A[a] + B[b] + C[c]
            scores.append(score)

scores.sort(reverse=True)

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

Submission status: Accepted

Solution code:
from itertools import product


X, Y, Z, K = map(int, input().split())
lst_A = list(map(int, input().split()))
lst_B = list(map(int, input().split()))
lst_C = list(map(int, input().split()))
lst_A.sort(reverse=True)
lst_B.sort(reverse=True)
lst_C.sort(reverse=True)

lst_C_K = lst_C[:K]


lst_AB = sorted([a+b for a, b in product(lst_A, lst_B)], reverse=True)
lst_AB_K = lst_AB[:K]

lst_ABC = sorted([ab+c for ab, c in product(lst_AB_K, lst_C_K)], reverse=True)
lst_ABC_K = lst_ABC[:K]

print(*lst_ABC_K, sep="\n")

Submission status: Accepted

Solution code:
import itertools

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)

D = [a+b for a,b in itertools.product(A[:K], B[:K])]
D.sort(reverse=True)

E = [c+d for c,d in itertools.product(C[:K], D[:K])]
E.sort(reverse=True)

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

Submission status: Accepted

Solution code:
def d_cake_123_binary_search(X, Y, Z, K, A, B, C):
    # editionalの解法4 O(K^2log(max(P))
    # 参考: https://atcoder.jp/contests/abc123/submissions/4871511
    import bisect
    ab = sorted([e1 + e2 for e2 in B for e1 in A])  # A, Bの要素は全部調べる

    # rejected 以上の値は、美味しさの合計がそれ以上である個数がK個未満である
    accepted, rejected = -1, 10**11
    while abs(accepted - rejected) > 1:
        mid = (accepted + rejected) // 2
        count = sum([len(ab) - bisect.bisect_left(ab, mid - e) for e in C])
        if count >= K:
            accepted = mid
        else:
            rejected = mid

    ans = []
    for e in C:
        idx = bisect.bisect_left(ab, accepted - e)
        for i in range(idx, len(ab)):
            ans.append(e + ab[i])
    ans.sort(reverse=True)
    return '\n'.join(map(str, ans[:K]))

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()]
print(d_cake_123_binary_search(X, Y, Z, K, A, B, C))

Submission status: Accepted

Solution code:
from heapq import heappush, heappop
s=set()
q=[]
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)
heappush(q, (-(a[0]+b[0]+c[0]), 0, 0, 0))
def push(d, e, f):
    if (d, e, f) not in s and 0<=d<x and 0<=e<y and 0<=f<z:
        heappush(q, (-(a[d]+b[e]+c[f]), d, e, f))
        s.add((d, e, f))
for i in range(k):
    p, d, e, f =heappop(q)
    print(-p)
    push(d+1, e, f)
    push(d, e+1, f)
    push(d, e, f+1)

Submission status: Accepted

Solution code:
Anum, Bnum, Cnum, 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)

yum = []
for ia in range(Anum):
    if(ia > K):
        break
    for ib in range(Bnum):
        if(ia * ib > K):
            break
        for ic in range(Cnum):
            if(ia * ib * ic > K):
                break
            yum.append(A[ia] + B[ib] + C[ic])
yum.sort(reverse=True)
for k in range(K):
    print(yum[k])

Submission status: Accepted

Solution code:
Anum, Bnum, Cnum, 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)

yum = []
for ia in range(Anum):
    for ib in range(Bnum):
        if(ia * ib > K):
            break
        for ic in range(Cnum):
            if(ia * ib * ic > K):
                break
            yum.append(A[ia] + B[ib] + C[ic])
yum.sort(reverse=True)
for k in range(K):
    print(yum[k])

Submission status: Accepted

Solution code:
x, y, z, k = map(int, input().split())
a_array = sorted([int(x) for x in input().split()], reverse=True)
b_array = sorted([int(x) for x in input().split()], reverse=True)
c_array = sorted([int(x) for x in input().split()], reverse=True)


def solver1():
    ab_array = sorted([x + y for x in a_array for y in b_array], reverse=True)[:3000]
    abc_array = sorted([ab + c for ab in ab_array for c in c_array], reverse=True)
    for abc in abc_array[:k]:
        print(abc)


solver1()

Submission status: Accepted

Solution code:
import sys
from itertools import product


read = sys.stdin.readline
X, Y, Z, K = map(int, read().split())
lst_A = list(map(int, read().split()))
lst_B = list(map(int, read().split()))
lst_C = list(map(int, read().split()))


lst_A.sort(reverse=True)
lst_B.sort(reverse=True)
lst_C.sort(reverse=True)
lst_C_K = lst_C[:K]


lst_AB = sorted([a+b for a, b in product(lst_A, lst_B)], reverse=True)
lst_AB_K = lst_AB[:K]


lst_ABC = sorted([ab+c for ab, c in product(lst_AB_K, lst_C_K)], reverse=True)
lst_ABC_K = lst_ABC[:K]


print(*lst_ABC_K, sep="\n")

Submission status: Accepted

Solution code:
import sys
from itertools import product

read = sys.stdin.readline
X, Y, Z, K = map(int, read().split())
lst_A = list(map(int, read().split()))
lst_B = list(map(int, read().split()))
lst_C = list(map(int, read().split()))


lst_A.sort(reverse=True)
lst_B.sort(reverse=True)
lst_C.sort(reverse=True)
lst_C_K = lst_C[:K]


lst_AB = sorted([a+b for a, b in product(lst_A, lst_B)], reverse=True)
lst_AB_K = lst_AB[:K]

lst_ABC = sorted([ab+c for ab, c in product(lst_AB_K, lst_C_K)], reverse=True)
lst_ABC_K = lst_ABC[:K]

for i in range(K):
    print(lst_ABC_K[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)

ABC = []

for i in range(x):
    for j in range(y):
        if (i + 1) * (j + 1)  > k:
            break
        for h in range(z):
            if (i + 1) * (j + 1) * (h + 1) > k:
                break
            ABC.append(A[i] + B[j] + C[h])


ABC.sort(reverse=True)

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

Submission status: Accepted

Solution code:
import numpy as np
def solve(a, b, c, k):
    x, y, z = len(a), len(b), len(c)
    A = a.reshape(x, 1) + b.reshape(1, y)
    d = np.sort(A.flatten())[::-1][:k]
    B = d.reshape(len(d), 1) + c.reshape(1, z)
    return np.sort(B.flatten())[::-1][:k]

x, y, z, k = map(int, input().split())
a = np.asarray(list(map(int, input().split())))
b = np.asarray(list(map(int, input().split())))
c = np.asarray(list(map(int, input().split())))
print("\n".join(map(str, solve(a, b, c, k))))

Submission status: Accepted

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

def f(thres:int)->bool:
    """return (おいしさが thres 以上の組み合わせ) >= K
    """
    global K
    cnt = 0
    for a in range(X):
        if A[a]+B[0]+C[0]<thres:
            break
        for b in range(Y):
            if A[a]+B[b]+C[0]<thres:
                break
            for c in range(Z):
                if A[a]+B[b]+C[c]<thres:
                    break
                cnt += 1
                if cnt >= K:
                    return True
    return False

def binary_search(f, s:int, t:int)->int:
    """f: function(x:int)->bool
    f(s)=False, f(t)=True，f は広義単調増加
    return : [s, t) での f(x)=True なる最小のx
    """
    ok = s-1
    ng = t
    while ng - ok > 1:
        mid = (ok + ng)//2
        if f(mid): ok = mid
        else:      ng = mid
        # print(ng, ok, ok-ng)

    if ok==s-1:
        raise(ValueError("For all x, f(x)=False"))
    return ok

M = A[0]+B[0]+C[0]
m = A[-1]+B[-1]+C[-1]
# print(f(m), f(M))
thres = binary_search(f, m, M+1)-1
# print("thres:",thres)
ans = []
for a in range(X):
    if A[a]+B[0]+C[0]<thres:
        break
    for b in range(Y):
        if A[a]+B[b]+C[0]<thres:
            break
        for c in range(Z):
            if A[a]+B[b]+C[c]<thres:
                break
            ans.append(A[a]+B[b]+C[c])

ans.sort(reverse=True)
print("\n".join(map(str, ans[:K])))

Submission status: Accepted

Solution code:
from itertools import product


X, Y, Z, K = map(int, input().split())
lst_A = list(map(int, input().split()))
lst_B = list(map(int, input().split()))
lst_C = list(map(int, input().split()))
lst_A.sort(reverse=True)
lst_B.sort(reverse=True)
lst_C.sort(reverse=True)
lst_C_K = lst_C[:K]


lst_AB = sorted([a+b for a, b in product(lst_A, lst_B)], reverse=True)
lst_AB_K = lst_AB[:K]

lst_ABC = sorted([ab+c for ab, c in product(lst_AB_K, lst_C_K)], reverse=True)
lst_ABC_K = lst_ABC[:K]

for i in range(K):
    print(lst_ABC_K[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)

ABC = []
for i in range(x):
    for j in range(y):
        if (i + 1) * (j + 1)  <= k:
            for h in range(z):
                if (i + 1) * (j + 1) * (h + 1) <= k:
                    ABC.append(A[i] + B[j] + C[h])
                else:
                    break    
        else:
            break


ABC.sort(reverse=True)

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

d=[]
for i in range(min(k,x)):
    for j in range(min(k,y)):
        d.append(a[i]+b[j])
d.sort(reverse=True)

e=[]
for i in range(min(k,x*y)):
    for j in range(min(k,z)):
        e.append(d[i]+c[j])
e.sort(reverse=True)

for i in range(min(k,x*y*z)):
    print(e[i])

Submission status: Accepted

Solution code:
import sys
from itertools import product


X, Y, Z, K = map(int, input().split())
lst_A = list(map(int, input().split()))
lst_B = list(map(int, input().split()))
lst_C = list(map(int, input().split()))
lst_A.sort(reverse=True)
lst_B.sort(reverse=True)
lst_C.sort(reverse=True)

# lst_A_K = lst_A[:K]
# lst_B_K = lst_B[:K]
lst_C_K = lst_C[:K]


lst_AB = sorted([a+b for a, b in product(lst_A, lst_B)], reverse=True)
lst_AB_K = lst_AB[:K]

lst_ABC = sorted([ab+c for ab, c in product(lst_AB_K, lst_C_K)], reverse=True)
lst_ABC_K = lst_ABC[:K]

print(*lst_ABC_K, sep="\n")

Submission status: Accepted

Solution code:
#!/usr/bin/env python3.4
# -*- coding: utf-8 -*-

# abc123_d
import itertools
import math

# input
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 = range(1000)
# B = range(1000)
# C = range(1000)
# getans
A.sort(reverse=True)
B.sort(reverse=True)
C.sort(reverse=True)
arr = []
for i in range(X):
    for j in range(Y):
        for k in range(Z):
            if (i+1)*(j+1)*(k+1) > K:
                break
            arr.append(A[i]+B[j]+C[k])
#print(len(arr))
arr.sort(reverse=True)
# output
ans = '\n'.join(map(str, arr[:K]))
print(ans)

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