Problem:


Score : 500 points

Problem Statement

Given are N integers A_1,\ldots,A_N.

We will choose exactly K of these elements. Find the maximum possible product of the chosen elements.

Then, print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Constraints

1 \leq K \leq N \leq 2\times 10^5

|A_i| \leq 10^9

Input

Input is given from Standard Input in the following format:

N K
A_1 \ldots A_N

Output

Print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Sample Input 1

4 2
1 2 -3 -4

Sample Output 1

12

The possible products of the two chosen elements are 2, -3, -4, -6, -8, and 12, so the maximum product is 12.

Sample Input 2

4 3
-1 -2 -3 -4

Sample Output 2

1000000001

The possible products of the three chosen elements are -24, -12, -8, and -6, so the maximum product is -6.

We print this value modulo (10^9+7), that is, 1000000001.

Sample Input 3

2 1
-1 1000000000

Sample Output 3

1000000000

The possible products of the one chosen element are -1 and 1000000000, so the maximum product is 1000000000.

Sample Input 4

10 10
1000000000 100000000 10000000 1000000 100000 10000 1000 100 10 1

Sample Output 4

999983200

Be sure to print the product modulo (10^9+7).



Sample input:
4 2
1 2 -3 -4


Sample output:
12

Submission status: Accepted

Solution code:
n, k = map(int, input().split())
a = list(map(int, input().split()))

a.sort(reverse=True, key=lambda x:abs(x))
cnt = 0
im = -1
ip = -1
cp = 0
mod = 10 ** 9 + 7
nm = 0
np = 0

for i, ai in enumerate(a):
    if i < k:
        if ai < 0:
            im = i
            cnt += 1
        if ai > 0:
            ip = i
    else:
        if ai < 0 and nm == 0:
            nm = ai
        if ai > 0 and np == 0:
            np = ai
    if ai > 0:
        cp += 1

ans = 1
f = 0

# print(a)
if cnt % 2 and k < n:
    if cp == 0:
        a.sort(reverse=True)
        for i, ai in enumerate(a):
            if i == k:
                break
            ans *= ai
            ans %= mod
        print(ans) # ok
    else:
        cnt = 0
        f1 = 0
        f2 = 0
        for i, ai in enumerate(a):
            if f1 + f2 + cnt == k:
                break 
            if i == im:
                f1 = 1
                continue
            if i == ip:
                f2 = 1
                continue
            if f1 and ai <= 0:
                continue
            if f2 and ai >= 0:
                continue
            ans *= ai
            ans %= mod
            cnt += 1
        if ip == -1:
            ans *= np
        else:
            ans *= max(a[ip] * np, a[im] * nm)
        ans %= mod
        print(ans) # ng
        # - + - - / + -
else:
    for i, ai in enumerate(a):
        if i == k:
            break
        ans *= ai
        ans %= mod
    print(ans) # ok

Submission status: Accepted

Solution code:
mod=10**9+7
n,k=map(int,input().split())
a=sorted(list(map(int,input().split())))
pi=1
ni=0
ans=1
i=0
while i<k-1:
  if a[ni]*a[ni+1]>a[-pi]*a[-pi-1]:
    ans=ans*a[ni]*a[ni+1]%mod
    ni+=2
    i+=2
  else:
    ans=ans*a[-pi]%mod
    pi+=1
    i+=1
if i==k-1:
  ans=ans*a[-pi]%mod
if a[-1]<0 and k%2==1:
  ans=1
  for i in a[n-k:]:
    ans=ans*i%mod
print(ans)

Submission status: Accepted

Solution code:
N, K = map(int, input().split())
A = sorted([int(a) for a in input().split()], key = lambda x: -abs(x))
P = 10 ** 9 + 7
m = 0
ans = 1
lp = 0
lm = 0
np = 0
nm = 0
for a in A[:K]:
    if a > 0:
        lp = a
        ans = ans * a % P
    elif a < 0:
        lm = a
        m ^= 1
        ans = ans * a % P
    else:
        print(0)
        exit()

if m == 0:
    print(ans)
    exit()

for a in A[K:]:
    if a > 0:
        np = a
        break
for a in A[K:]:
    if a < 0:
        nm = a
        break

if lp and nm and lm and np:
    if lp * np > lm * nm:
        print(ans * pow(lm, P-2, P) * np % P)
    else:
        print(ans * pow(lp, P-2, P) * nm % P)
elif lp and nm:
    print(ans * pow(lp, P-2, P) * nm % P)
elif lm and np:
    print(ans * pow(lm, P-2, P) * np % P)
else:
    A = A[::-1][:K]
    ans = 1
    for a in A:
        ans = ans * a % P
    print(ans)

Submission status: Accepted

Solution code:
from bisect import bisect_left
N,K=map(int, input().split())
A=list(map(int, input().split()))
p=10**9+7
A=sorted(A)
thresh=bisect_left(A,0)
minus=A[:thresh]
plus=A[thresh:][::-1]

#print(plus, minus)
if len(plus)==0:
    ans=1
    if K%2!=0:
        minus=minus[::-1]
        for i in range(K):
            ans*=minus[i]
            ans%=p
    else:
        for i in range(K):
            ans*=minus[i]
            ans%=p
    print(ans)
    exit()

if len(minus)==0:
    ans=1
    for i in range(K):
        ans*=plus[i]
        ans%=p
    print(ans)
    exit()

midx=0
pidx=0
ans=1

while K>0 and (0<=midx<len(minus) or 0<=pidx<len(plus)):
    if midx==len(minus)-1:
        nexmin=minus[midx]
    elif midx>=len(minus):
        nexmin=-1
    else:
        if K>=2:
            nexmin=minus[midx]*minus[midx+1]
        else:
            nexmin=minus[midx]

    if pidx==len(plus)-1:
        nexplus=plus[pidx]
        fact=nexplus
    elif pidx>=len(plus):
        nexplus=-float("INF")
        fact=nexplus
    else:
        #if plus[pidx+1]!=0:
        #    nexplus=plus[pidx]*plus[pidx+1]
        #else:
        #    nexplus=plus[pidx]
        if K>=2:
            nexplus=plus[pidx]*plus[pidx+1]
        else:
            nexplus=plus[pidx]
        fact=plus[pidx]

    if nexmin>=nexplus:
        ans*=nexmin
        ans%=p
        midx+=2
        K-=2
    else:
        ans*=fact
        ans%=p
        pidx+=1
        K-=1


print(ans)

Submission status: Accepted

Solution code:
p=10**9+7
n,k=map(int,input().split())
a=sorted(list(map(int,input().split())))
pi=1
ni=0
ans=1
i=0
while i<k-1:
  if a[ni]*a[ni+1]>a[-pi]*a[-pi-1]:
    ans=ans*a[ni]*a[ni+1]%p
    ni+=2
    i+=2
  else:
    ans=ans*a[-pi]%p
    pi+=1
    i+=1
if i==k-1:
  ans=ans*a[-pi]%p
if a[-1]<0 and k%2==1:
  ans=1
  for i in a[n-k:]:
    ans=ans*i%p
print(ans)

Submission status: Accepted

Solution code:
from bisect import bisect_left,bisect_right
p=10**9+7
n,k=map(int,input().split())
a=sorted(list(map(int,input().split())))
pi=1
ni=0
ans=1
i=0
while i<k-1:
  if a[ni]*a[ni+1]>a[-pi]*a[-pi-1]:
    ans=ans*a[ni]*a[ni+1]%p
    ni+=2
    i+=2
  else:
    ans=ans*a[-pi]%p
    pi+=1
    i+=1
if i==k-1:
  ans=ans*a[-pi]%p
if a[-1]<0 and k%2==1:
  ans=1
  for i in a[n-k:]:
    ans=ans*i%p
print(ans)

Submission status: Accepted

Solution code:
#! /usr/bin/env python3

import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
sys.setrecursionlimit(500000)
MOD = pow(10, 9) + 7

N, K, *A = map(int, read().split())

if K == N:
    ans = 1
    for a in A:
        ans = ans * a % MOD
    print(ans)
    sys.exit()

A_pos = [a for a in A if a >= 0]
A_neg = [a for a in A if a < 0]

if len(A_pos) == 0:
    if K % 2 == 1:
        A_neg.sort(reverse=True)
    else:
        A_neg.sort()
    ans = 1
    for a in A_neg[:K]:
        ans = ans * a % MOD
    print(ans)
    sys.exit()

A_pos.sort()
A_neg.sort(reverse=True)
ans = 1
r = K
if r % 2 == 1:
    ans = ans * A_pos.pop() % MOD
    r -= 1

while r > 0:
    if len(A_pos) <= 1:
        ans = ans * A_neg.pop() * A_neg.pop() % MOD
    elif len(A_neg) <= 1:
        ans = ans * A_pos.pop() * A_pos.pop() % MOD

    else:
        acc_pos = A_pos[-1] * A_pos[-2]
        acc_neg = A_neg[-1] * A_neg[-2]

        if acc_pos > acc_neg:
            ans = ans * A_pos.pop() * A_pos.pop() % MOD
        else:
            ans = ans * A_neg.pop() * A_neg.pop() % MOD
    r -= 2
print(ans % MOD)

Submission status: Accepted

Solution code:
mod = 10**9 + 7
n, k = map(int, input().split())
a = list(map(int, input().split()))
a.sort()
index_change = 0
ans = 1
for i in range(n-1):
    if a[i] <= 0 and a[i+1] > 0:
        index_change = i+1
        break
else:
    if k % 2 == 1:
        for i in range(1, k+1):
            ans *= a[-i]
            ans %= mod
    else:
        for i in range(k):
            ans *= a[i]
            ans %= mod
    print(ans)
    exit()
l = 0
r = n-1
while k > 0:
    if k == 1:
        if r >= index_change:
            ans *= a[r]
            ans %= mod
            break
        else:
            ans *= a[l]*a[l+1]
            ans %= mod
            ans *= pow(a[r+1], mod-2, mod)
            ans %= mod
            break
    else:
        left = a[l]*a[l+1]
        right = a[r]*a[r-1]
        if left >= right:
            ans *= left
            ans %= mod
            l += 2
            k -= 2
        else:
            ans *= a[r]
            ans %= mod
            r -= 1
            k -= 1
print(ans)

Submission status: Accepted

Solution code:
n, k = map(int, input().split())
modulo = 10 ** 9 + 7
*arr, = map(int, input().split())
inverses = [pow(v, modulo - 2, modulo) for v in arr]
neg_cnt = 0
for v in arr:
    if v < 0:
        neg_cnt += 1

def min_pos(arr):
    pass


if k == n:
    res = 1
    for v in arr:
        res *= v
        res %= modulo
    print(res)
elif neg_cnt == n and k % 2 == 1:
    res = 1
    arr.sort(reverse=True)
    for i in range(k):
        res *= arr[i]
        res %= modulo
    print(res)
else:
    pos = []
    neg = []
    for i, v in enumerate(arr):
        if v < 0:
            neg.append(i)
        else:
            pos.append(i)

    neg.sort(key=lambda v: abs(arr[v]), reverse=True)
    pos.sort(key=lambda v: abs(arr[v]), reverse=True)


    if k % 2:
        res = arr[pos[0]]
        i = 1
    else:
        res = 1
        i = 0
    j = 0
    while i + j < k and (i < len(pos) - 1 or j < len(neg) - 1):
        if j >= len(neg) - 1 or i < len(pos) - 1 and arr[pos[i]] * arr[pos[i + 1]] > arr[neg[j]] * arr[neg[j + 1]]:
            res *= arr[pos[i]]
            res *= arr[pos[i + 1]]
            i += 2
        else:
            res *= arr[neg[j]]
            res *= arr[neg[j + 1]]
            j += 2
        res %= modulo

    while i + j < k:
        res *= arr[pos[i]]
        i += 1
        res %= modulo

    print(res)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
from collections import *

N, K = map(int, input().split())
A = list(map(int, input().split()))
MOD = 10**9+7
p, n = [], []

for Ai in A:
    if Ai>=0:
        p.append(Ai)
    else:
        n.append(Ai)

if len(p)==0 and K%2==1:
    if 0 in A:
        print(0)
    else:
        n.sort(reverse=True)
        ans = 1
        
        for ni in n[:K]:
            ans *= ni
            ans %= MOD
        
        print(ans)
    exit()
    
if K==N:
    ans = 1
    
    for Ai in A:
        ans *= Ai
        ans %= MOD
    
    print(ans)
    exit()

p.sort(reverse=True)
n.sort()

if K%2==0:
    l = []
    
    for i in range(len(p)//2):
        l.append(p[2*i]*p[2*i+1])
    
    for i in range(len(n)//2):
        l.append(n[2*i]*n[2*i+1])

    l.sort(key=lambda x: abs(x), reverse=True)
    ans = 1
    
    for i in range(K//2):
        ans *= l[i]
        ans %= MOD
else:
    ans = p[0]
    p = p[1:]
    l = []
    
    for i in range(len(p)//2):
        l.append(p[2*i]*p[2*i+1])
    
    for i in range(len(n)//2):
        l.append(n[2*i]*n[2*i+1])
    
    l.sort(key=lambda x: abs(x), reverse=True)
    
    for i in range((K-1)//2):
        ans *= l[i]
        ans %= MOD

print(ans)

Submission status: Accepted

Solution code:
n,k = map(int, input().split())
a =list(map(int, input().split()))
ans =1

if n == k:
   for i in a:
       ans *= i
       if abs(ans) >10**9+7:
           ans = ans%(10**9+7)

elif all(i <= 0 for i in a) and k%2 ==1:
    a.sort(reverse = True)
    for i in range(k):
        ans *= a[i]
        if abs(ans) > 10 ** 9 + 7:
            ans = ans % (10 ** 9 + 7)

else:
    am =[]
    ap =[]

    a.sort(key = abs,reverse = True)
    amax = a[:k]
    amin = a[k:]
    c=1
    if 0 in amax:
        ans = 0
    else:
        for i in amax:
            if i<0:
                am.append(i)
                c *=-1
            elif i>0:
                ap.append(i)
        if c ==1:
            for i in amax:
                ans *= i
                if abs(ans) > 10 ** 9 + 7:
                    ans = ans % (10 ** 9 + 7)
        else:
            if ap == []:
                amax.remove(max(am))
                amax.append(max(amin))

            elif max(am)*min(amin) < min(ap)*max(amin):
                amax.remove(max(am))
                amax.append(max(amin))
            else:
                amax.remove(min(ap))
                amax.append(min(amin))
            for i in amax:
                ans *= i
                if abs(ans) > 10 ** 9 + 7:
                    ans = ans % (10 ** 9 + 7)

print(ans % (10 ** 9 + 7))

Submission status: Accepted

Solution code:
n,k = map(int,input().split())
A = list(map(int,input().split()))
mod = 10**9+7
plus = []
minus=[]
for i in A:
    if i>=0:
        plus.append(i)
    else:
        minus.append(i)
ok = False
if len(plus)>0:
    if n==k:
        ok = (len(minus)%2==0)
    else:
        ok = True
else:
    ok = (k%2==0)
ans = 1
if not ok:
    A.sort(key=abs)
    for i in range(k):
        ans *= A[i]
        ans %= mod
else:
    plus.sort()
    minus.sort(reverse=True)
    if k%2 == 1:
        ans *= plus.pop()
    P = []
    while len(plus) >= 2:
        P.append((plus.pop())*(plus.pop()))
    while len(minus) >= 2:
        P.append((minus.pop())*(minus.pop()))
    P.sort(reverse=True)
    for i in range(k//2):
        ans *= P[i]
        ans %= mod
print(ans)

Submission status: Accepted

Solution code:
from collections import deque
# N = int(input())
N, K = [int(_) for _ in input().split()]
A = [int(_) for _ in input().split()]
MOD = 10 ** 9 + 7
A_p = []
A_n = []
for a in A:
  if a >= 0:
    A_p.append(a)
  else:
    A_n.append(-a)

A_p.sort(reverse=True)
A_n.sort(reverse=True)
A_p = deque(A_p)
A_n = deque(A_n)

p_top = 0
n_top = 0
ans_p = deque([])
ans_n = deque([])
for i in range(K):
  if len(A_p) > 0 and len(A_n) > 0 and A_p[0] >= A_n[0]:
    ans_p.append(A_p.popleft())
  elif len(A_n) > 0:
    ans_n.append(A_n.popleft())
  elif len(A_p) > 0:
    ans_p.append(A_p.popleft())
if len(ans_n) % 2 == 1:
  if len(ans_p) > 0 and len(ans_n) > 0 and len(A_p) > 0 and len(A_n) > 0 and ans_p[-1] * A_p[0] >= ans_n[-1] * A_n[0]:
    ans_n.pop()
    ans_p.append(A_p.popleft())
  elif len(ans_p) > 0 and len(A_n) > 0:
    ans_p.pop()
    ans_n.append(A_n.popleft())
  elif len(ans_n) > 0 and len(A_p) > 0:
    ans_n.pop()
    ans_p.append(A_p.popleft())
ans = 1
for a in ans_p:
  ans = (a * ans) % MOD
for a in ans_n:
  ans = (-a * ans) % MOD
if ans != 0 and len(ans_n) % 2 == 1:
  ans = 1
  A_abs = [abs(a) for a in A]
  A_abs.sort()
  for i in range(K):
    ans = (ans * A_abs[i]) % MOD
  ans = (-ans) % MOD
print(ans)

Submission status: Accepted

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

N, K = map(int, input().split())
A = list(map(int, input().split()))
MOD = 10**9+7
p, n = [], []

for i in range(N):
    if A[i]>=0:
        p.append(A[i])
    else:
        n.append(A[i])

ok = False

if len(p)>0:
    if N==K:
        if len(n)%2==0:
            ok = True
    else:
        ok = True
else:
    if K%2==0:
        ok = True

if not ok:
    A.sort(key=lambda x: abs(x))
    ans = 1
    
    for Ai in A[:K]:
        ans *= Ai
        ans %= MOD

    print(ans)
    exit()

p.sort(reverse=True)
n.sort()

if K%2==1:
    ans = p[0]
    p = p[1:]
else:
    ans = 1
    
l = []
    
for i in range(len(p)//2):
    l.append(p[2*i]*p[2*i+1])
    
for i in range(len(n)//2):
    l.append(n[2*i]*n[2*i+1])

l.sort(key=lambda x: abs(x), reverse=True)

for li in l[:K//2]:
    ans *= li
    ans %= MOD
    
print(ans)

Submission status: Accepted

Solution code:
from collections import deque
# N = int(input())
N, K = [int(_) for _ in input().split()]
A = [int(_) for _ in input().split()]
MOD = 10 ** 9 + 7
A_p = []
A_n = []
for a in A:
  if a >= 0:
    A_p.append(a)
  else:
    A_n.append(-a)

A_p.sort(reverse=True)
A_n.sort(reverse=True)
A_p = deque(A_p)
A_n = deque(A_n)

p_top = 0
n_top = 0
ans_p = deque([])
ans_n = deque([])
for i in range(K):
  if len(A_p) == 0:
    ans_n.append(A_n.popleft())
  elif len(A_n) == 0:
    ans_p.append(A_p.popleft())
  elif A_p[0] >= A_n[0]:
    ans_p.append(A_p.popleft())
  else:
    ans_n.append(A_n.popleft())
if len(ans_n) % 2 == 1:
  if len(ans_p) > 0 and len(ans_n) > 0 and len(A_p) > 0 and len(A_n) > 0 and ans_p[-1] * A_p[0] >= ans_n[-1] * A_n[0]:
    ans_n.pop()
    ans_p.append(A_p.popleft())
  elif len(ans_p) > 0 and len(A_n) > 0:
    ans_p.pop()
    ans_n.append(A_n.popleft())
  elif len(ans_n) > 0 and len(A_p) > 0:
    ans_n.pop()
    ans_p.append(A_p.popleft())
ans = 1
for a in ans_p:
  ans = (a * ans) % MOD
for a in ans_n:
  ans = (-a * ans) % MOD
if ans != 0 and len(ans_n) % 2 == 1:
  ans = 1
  A_abs = [abs(a) for a in A]
  A_abs.sort()
  for i in range(K):
    ans = (ans * A_abs[i]) % MOD
  ans = (-ans) % MOD
print(ans)

Submission status: Accepted

Solution code:
n, k = map(int, input().split())
*A, = map(int, input().split())
p = 10**9 + 7
A.sort()
ans = 1
if A[n - 1] <= 0 and k % 2 == 1:
    for i in range(k):
        ans *= A[n - 1 - i]
        ans %= p
    print(ans)
    exit()
i = 0
j = n - 1
if k % 2 == 1:
    ans *= A[j]
    ans %= p
    j -= 1
    k -= 1
for _ in range(k // 2):
    left = A[i] * A[i + 1]
    right = A[j] * A[j - 1]
    if (left > right):
        ans *= left
        ans %= p
        i += 2
    else:
        ans *= right
        ans %= p
        j -= 2
print(ans)

Submission status: Accepted

Solution code:
N, K = map(int, input().split())
A = list(map(int, input().split()))
m = 10**9+7
pos = [*filter(lambda x: x>=0, A)]
neg = [*filter(lambda x: x<0, A)]
pos.sort(reverse=True)
neg.sort()

ans = 1
i,j = 0,0
while i+j < K:
    flag = True
    if i == len(pos):
        flag = False
    elif j == len(neg):
        flag = True
    elif pos[i] < -neg[j]:
        flag = False

    if flag:
        ans = ans * pos[i] % m
        i += 1
    else:
        ans = ans * neg[j] % m
        j += 1

if j % 2 == 0 or N==K:
    print(ans)
elif len(pos) == 0:
    ans = 1
    for i in range(K):
        ans = ans * neg[len(neg)-1-i] % m
    print(ans)
else:
    flag2 = True
    if i == 0:
        flag2 = True
    elif j == 0:
        flag2 = False
    elif i == len(pos):
        flag2 = False
    elif j == len(neg):
        flag2 = True
    elif pos[i-1]*pos[i] < neg[j-1]*neg[j]:
        flag2 = False

    if flag2:
        ans = (ans * pow(neg[j-1],m-2,m) % m) * pos[i] % m
    else:
        ans = (ans * pow(pos[i-1],m-2,m) % m) * neg[j] % m
    print(ans)

Submission status: Accepted

Solution code:
from collections import deque
# N = int(input())
N, K = [int(_) for _ in input().split()]
A = [int(_) for _ in input().split()]
MOD = 10 ** 9 + 7
A_p = []
A_n = []
for a in A:
  if a >= 0:
    A_p.append(a)
  else:
    A_n.append(-a)

A_p.sort(reverse=True)
A_n.sort(reverse=True)
A_p = deque(A_p)
A_n = deque(A_n)

p_top = 0
n_top = 0
ans_p = deque([])
ans_n = deque([])
for i in range(K):
  if len(A_p) == 0:
    ans_n.append(A_n.popleft())
  elif len(A_n) == 0:
    ans_p.append(A_p.popleft())
  elif A_p[0] >= A_n[0]:
    ans_p.append(A_p.popleft())
  else:
    ans_n.append(A_n.popleft())
if len(ans_n) % 2 == 1:
  if len(ans_p) == 0 and len(A_p) > 0:
    ans_n.pop()
    ans_p.append(A_p.popleft())
  elif len(ans_n) == 0 and len(A_n) > 0:
    ans_p.pop()
    ans_n.append(A_n.popleft())
  elif len(ans_p) > 0 and len(ans_n) > 0 and len(A_p) > 0 and len(A_n) > 0 and ans_p[-1] * A_p[0] >= ans_n[-1] * A_n[0]:
    ans_n.pop()
    ans_p.append(A_p.popleft())
  elif len(ans_p) > 0 and len(A_n) > 0:
    ans_p.pop()
    ans_n.append(A_n.popleft())
  elif len(ans_n) > 0 and len(A_p) > 0:
    ans_n.pop()
    ans_p.append(A_p.popleft())
ans = 1
for a in ans_p:
  ans = (a * ans) % MOD
for a in ans_n:
  ans = (-a * ans) % MOD
if ans != 0 and len(ans_n) % 2 == 1:
  ans = 1
  A_abs = [abs(a) for a in A]
  A_abs.sort()
  for i in range(K):
    ans = (ans * A_abs[i]) % MOD
  ans = (-ans) % MOD
print(ans)

Submission status: Accepted

Solution code:
import sys

def LI(): return list(map(int,sys.stdin.readline().rstrip().split()))  #空白あり
def S(): return sys.stdin.readline().rstrip()

N,K = map(int,S().split())
A = LI()
mod = 10**9+7

ans = 1

if N == K:
    for i in range(N):
        ans *= A[i]
        ans %= mod
    print(ans)
    exit()

B = []  # 非負の要素
C = []  # 負の要素
for i in range(N):
    if A[i] >= 0:
        B.append(A[i])
    else:
        C.append(A[i])
b = len(B)  # 非負の要素の個数
c = len(C)  # 負の要素の個数

if c == N and K % 2 == 1:
    A.sort(reverse=True)
    for i in range(K):
        ans *= A[i]
        ans %= mod
    print(ans)
    exit()

# 以下、K個の積を非負にできる場合のみ残る

B.sort(reverse=True)
C.sort()
d = 0  # Bから選んだ個数
e = 0  # Cから選んだ個数

# ansを非負に維持しながら、Bの要素を1個ずつ、もしくはCの要素を2個ずつ掛け合わせていく

while d + e < K:
    if d + e == K-1:
        ans *= B[d]
        ans %= mod
        d += 1
    else:
        if e >= c-1:
            ans *= B[d]
            ans %= mod
            d += 1
        elif d >= b-1:
            ans *= C[e]*C[e+1]
            ans %= mod
            e += 2
        else:
            if B[d]*B[d+1] < C[e]*C[e+1]:
                ans *= C[e]*C[e+1]
                ans %= mod
                e += 2
            else:
                ans *= B[d]
                ans %= mod
                d += 1

print(ans)

Submission status: Accepted

Solution code:
import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, tan, asin, acos, atan, radians, degrees, log2, gcd
from itertools import accumulate, permutations, combinations, combinations_with_replacement, product, groupby
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect, bisect_left, insort, insort_left
from heapq import heappush, heappop
from functools import reduce
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def ZIP(n): return zip(*(MAP() for _ in range(n)))
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
mod = 10 ** 9 + 7 
#mod = 998244353
from decimal import *
#import numpy as np
#decimal.getcontext().prec = 10

N, K = MAP()
A = LIST()

if N == K:
	ans = 1
	for x in A:
		ans = ans*x%mod
	print(ans)
	exit()

a = []
for x in A:
	flg = 0
	if x < 0:
		flg = 1
	a.append([x, abs(x), flg])

a.sort(key = lambda x: -x[1])

#print(a)

flg_sum = sum([x[2] for x in a[:K]])

if flg_sum%2 == 0:
	ans = 1
	for x in a[:K]:
		ans = ans*x[1]%mod
	print(ans)
	exit()


flg = a[K-1][2]
s0 = 0
s1 = 0
for i in range(K, N):
	if a[i][2] != flg:
		s0 = a[K-1][1]
		s1 = a[i][1]
		break

flg = a[K][2]
t0 = 0
t1 = 0
for i in range(K-1, -1, -1):
	if a[i][2] != flg:
		t0 = a[i][1]
		t1 = a[K][1]
		break

if s0+t0 != 0:
	ans = 1
	if s0 == 0:
		for i in range(K):
			if a[i][1] != t0:
				ans = ans*a[i][1]%mod
		print(ans*t1%mod)
		exit()
	elif t0 == 0:
		for i in range(K-1):
			ans = ans*a[i][1]%mod
		print(ans*s1%mod)
		exit()
	elif s1*t0 >= s0*t1 or t0 == 0:
		for i in range(K-1):
			ans = ans*a[i][1]%mod
		print(ans*s1%mod)
		exit()
	else:
		for i in range(K):
			if a[i][1] != t0:
				ans = ans*a[i][1]%mod
		print(ans*t1%mod)
		exit()


ans = 1
for x in a[::-1][:K]:
	ans = ans*x[0]%mod

print(ans)

Submission status: Accepted

Solution code:
n, k = map(int,input().split())
a = list(map(int,input().split()))
mod = 10**9 + 7

plus = []
minus = []

for i in a:
	if i >= 0:
		plus.append(i)
	else:
		minus.append(i)

plus.sort(key = lambda x:-x)
minus.sort()

#print(plus, minus)

"""
貪欲チックに求める
numplus … 前からnumplus番目まで掛け合わせる
numminus … 前からnumminus番目まで掛け合わせる

入力例2に合わせるのは場合分けが必要だが, minusは2個単位で管理する.
"""

numplus = k
numminus = 0

"""
kがplusを超える場合, うまく処理ができないのでリスト参照できる範囲まで下げる.
"""
while numplus > len(plus):
	numplus -= 2
	numminus += 2

#print(numplus, numminus)

while numplus-2 >= 0 and numminus+1 < len(minus):
	if plus[numplus-1] * plus[numplus-2] <= minus[numminus] * minus[numminus+1]:
		numplus -= 2
		numminus += 2
	else:
		break

#print(numplus, numminus)

ans = 1

if numplus >= 0 and numminus >= 0 and numminus <= len(minus):
	for i in range(numplus):
		ans = ans * plus[i] % mod
	for i in range(numminus):
		ans = ans * minus[i] % mod
else:
	"""
	これは, ansが負になる場合や, minusが1個だけの場合, minusしかない場合, plusしかない場合に使える.
	"""
	#print("ここに来ました！")
	tmp = sorted(a, key=lambda x:-x)
	for i in range(k):
		ans = ans * tmp[i]%mod

print(ans)

Submission status: Accepted

Solution code:
MOD = 10**9 + 7
INF = 10**9 + 7


class modint():
    def __init__(self, value):
        self.value = value % MOD

    def __int__(self):
        return int(self.value)

    def __float__(self):
        return float(self.value)

    def __str__(self):
        return str(self.value)

    def __repr__(self):
        return str(self.value)

    def __add__(self, other):
        return (modint(self.value + other.value) if isinstance(other, modint)
                else modint(self.value + other))

    def __sub__(self, other):
        return (modint(self.value - other.value) if isinstance(other, modint)
                else modint(self.value - other))

    def __mul__(self, other):
        return (modint(self.value * other.value) if isinstance(other, modint)
                else modint(self.value * other))

    def __truediv__(self, other):
        return (modint(self.value * pow(other.value, MOD - 2, MOD))
                if isinstance(other, modint)
                else modint(self.value * pow(other, MOD - 2, MOD)))

    def __pow__(self, other):
        return (modint(pow(self.value, other.value, MOD))
                if isinstance(other, modint)
                else modint(pow(self.value, other, MOD)))

    def __eq__(self, other):
        return (self.value == other.value if isinstance(other, modint)
                else self.value == (other % MOD))

    def __ne__(self, other):
        return (self.value == other.value if isinstance(other, modint)
                else self.value == (other % MOD))

    def __radd__(self, other):
        return (modint(other.value + self.value) if isinstance(other, modint)
                else modint(other + self.value))

    def __rsub__(self, other):
        return (modint(other.value - self.value) if isinstance(other, modint)
                else modint(other - self.value))

    def __rmul__(self, other):
        return (modint(other.value * self.value) if isinstance(other, modint)
                else modint(other * self.value))

    def __rtruediv__(self, other):
        return (modint(other.value * pow(self.value, MOD - 2, MOD))
                if isinstance(other, modint)
                else modint(other * pow(self.value, MOD - 2, MOD)))

    def __rpow__(self, other):
        return (modint(pow(other.value, self.value, MOD))
                if isinstance(other, modint)
                else modint(pow(other, self.value, MOD)))

    def modinv(self):
        return modint(pow(self.value, MOD - 2, MOD))


def main():
    N, K = (int(i) for i in input().split())
    A = [int(i) for i in input().split()]
    ans = modint(1)
    if N == K:
        for a in A:
            ans *= a
        return print(ans)
    elif all(a < 0 for a in A) and K % 2 == 1:
        A.sort(key=abs)
        for a in A[:K]:
            ans *= a
        return print(ans)
    # 以降，非負の答えにできる
    A.sort(reverse=True, key=abs)
    if sum(a < 0 for a in A[:K]) % 2 == 0:
        for a in A[:K]:
            ans *= a
    else:
        ans1 = modint(1)  # 正を取り除く
        ans2 = modint(1)  # 負を取り除く
        p_remove = False
        x1 = INF
        for a in A[:K][::-1]:
            if a > 0 and not p_remove:
                p_remove = True
                x1 = a
                continue
            ans1 *= a
        n_remove = False
        x2 = INF
        for a in A[:K][::-1]:
            if a < 0 and not n_remove:
                n_remove = True
                x2 = a
                continue
            ans2 *= a
        y1 = 0  # 一番大きい負
        y2 = 0  # 一番大きい正
        for a in A[K:]:
            if y1 == 0 and a < 0:
                y1 = a
            if y2 == 0 and a > 0:
                y2 = a
            if y1 != 0 and y2 != 0:
                break
        ans1 *= y1
        ans2 *= y2
        if x1 != INF and x2 != INF:
            if abs(x2*y1) <= abs(x1*y2):
                ans = ans2
            else:
                ans = ans1
        elif x1 == INF and x2 == INF:
            # all 0
            ans = 0
        elif x1 == INF:
            # A[:K]に正の整数がなかった
            ans = ans2
        else:
            # A[:K]に負の整数がなかった
            ans = ans1
    print(ans)


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
N, K = map(int, input().split())
A = list(map(int, input().split()))
m = 10**9+7
pos = [*filter(lambda x: x>=0, A)]
neg = [*filter(lambda x: x<0, A)]
pos.sort(reverse=True)
neg.sort()

ans = 1
i,j = 0,0# 使った数
while i+j < K:
    flag = True
    if i == len(pos):
        flag = False
    elif j == len(neg):
        flag = True
    elif pos[i] >= -neg[j]:
        flag = True
    else:
        flag = False

    if flag:
        ans = ans * pos[i] % m
        i += 1
    else:
        ans = ans * neg[j] % m
        j += 1

if j % 2 == 0 or N==K:
    print(ans)
elif len(pos) == 0:
    ans = 1
    for i in range(K):
        ans = ans * neg[len(neg)-1-i] % m
    print(ans)
else:
    flag2 = True
    if i == 0:
        flag2 = True
    elif j == 0:
        flag2 = False
    elif i == len(pos):
        flag2 = False
    elif j == len(neg):
        flag2 = True
    elif pos[i-1]*pos[i] > neg[j-1]*neg[j]:# = を抜いた
        flag2 = True
    else:
        flag2 = False

    if flag2:
        ans = ans * pow(neg[j-1],m-2,m) % m
        ans = ans * pos[i] % m
    else:
        ans = ans * pow(pos[i-1],m-2,m) % m
        ans = ans * neg[j] % m
    print(ans)