Problem:
 Score : 400 points    Problem Statement There are N pieces of sushi. Each piece has two parameters: "kind of topping" t_i and "deliciousness" d_i .
You are choosing K among these N pieces to eat.
Your "satisfaction" here will be calculated as follows:   The satisfaction is the sum of the "base total deliciousness" and the "variety bonus".  The base total deliciousness is the sum of the deliciousness of the pieces you eat.  The variety bonus is x*x , where x is the number of different kinds of toppings of the pieces you eat.   You want to have as much satisfaction as possible.
Find this maximum satisfaction.      Constraints  1 \leq K \leq N  \leq 10^5  1 \leq t_i \leq N  1 \leq d_i \leq 10^9  All values in input are integers.         Input Input is given from Standard Input in the following format:  N  K  t_1  d_1  t_2  d_2  .  .  .  t_N  d_N       Output Print the maximum satisfaction that you can obtain.        Sample Input 1 5 3
1 9
1 7
2 6
2 5
3 1      Sample Output 1 26  If you eat Sushi 1,2 and 3 :   The base total deliciousness is 9+7+6=22 .  The variety bonus is 2*2=4 .   Thus, your satisfaction will be 26 , which is optimal.       Sample Input 2 7 4
1 1
2 1
3 1
4 6
4 5
4 5
4 5      Sample Output 2 25  It is optimal to eat Sushi 1,2,3 and 4 .       Sample Input 3 6 5
5 1000000000
2 990000000
3 980000000
6 970000000
6 960000000
4 950000000      Sample Output 3 4900000016  Note that the output may not fit into a 32 -bit integer type.

Solution (Python):
from heapq import heappush, heappop, heapreplace

INF = 10 ** 9 + 5

N, K, *TD = map(int, open(0).read().split())

E = [[] for _ in range(N)]
for t, d in zip(*[iter(TD)] * 2):
    E[t - 1].append(d)

for e in E:
    if e:
        e.sort(reverse=True)
    else:
        e.append(-INF)
E.sort(key=lambda x: -x[0])

cur = 0
Q = []
for ei in E[:K]:
    cur += ei[0]
    for eij in ei[1:]:
        heappush(Q, -eij)

for ei in E[K:]:
    for eij in ei:
        heappush(Q, -eij)

res = cur + K * K
for x in reversed(range(1, K)):
    v, w = E[x][0], -Q[0]
    if v < w:
        heappop(Q)
        cur += w
        heappush(Q, -v)
        cur -= v

    res = max(res, cur + x * x)

print(res)

Solution (Python):
from sys import stdin
from collections import defaultdict
from heapq import heappush, heappop

N, K = [int(x) for x in stdin.readline().rstrip().split()]
S = [[int(x) for x in stdin.readline().rstrip().split()] for _ in range(N)]
d = defaultdict(list)

for i in range(N):
    S[i][0] -= 1
    d[S[i][0]].append(S[i][1])

max_d = [None] * N

for k, v in d.items():
    max_d[k] = max(v)

S.sort(key=lambda x: x[1], reverse=True)
priority_queue1 = []
flag = [0] * N
ans = 0

for ti, di in S[:K]:
    ans += di
    flag[ti] = 1

    if di != max_d[ti]:
        heappush(priority_queue1, di)

syuruisuu = flag.count(1)
ans += syuruisuu ** 2
ans_l = [ans]
priority_queue2 = []

for i in range(N):
    if flag[i] == 0 and max_d[i] != None:
        heappush(priority_queue2, -max_d[i])

while len(priority_queue1) and len(priority_queue2):
    add_sushi = -heappop(priority_queue2)
    remove_sushi = heappop(priority_queue1)
    ans_cand = ans_l[-1] - syuruisuu**2 + (syuruisuu+1)**2 + add_sushi - remove_sushi
    ans_l.append(ans_cand)
    syuruisuu += 1

print(max(ans_l))

Solution (Python):
import heapq
N, K = map(int, input().split())
S = [[] for _ in range(N)]
E = [0] * N
Q = []
D = []
x = 0
k = 0
h = 0
for i in range(N):
  t, d = map(int, input().split())
  S[i] = [d, t]
S.sort(reverse=True)
for d, t in S:
  if E[t - 1] > 0:
    D.append(d)
  elif k < K:
    E[t - 1] += 1
    heapq.heappush(Q, d)
    x += 1
    k += 1
    h += d
h += x ** 2
for d in D:
  if k < K:
    heapq.heappush(Q, d)
    h += d
    k += 1
    continue
  q = heapq.heappop(Q)
  if d <= q:
    break
  _h = h - q - x ** 2 + d + (x - 1) ** 2
  if _h < h:
    break
  heapq.heappush(Q, d)
  x -= 1
  h = _h
print(h)

Solution (Python):
import heapq
from collections import deque
n,k=map(int,input().split())
l=[list(map(int,input().split())) for i in range(n)]

for i in range(n):
  l[i].reverse()
  l[i][0]*=-1
heapq.heapify(l)

check=[0 for i in range(10**5+1)]
L=[]
L2=[]
L2=deque(L2)
ans=[]

for i in range(k):
  x=heapq.heappop(l)
  if check[x[1]]==0:
    L.append(-x[0])
    check[x[1]]=1
  else:
    L2.append(-x[0])
p=sum(check)
ans.append(sum(L)+sum(L2)+p**2)

y=n-k
while y!=0:
  x=heapq.heappop(l)
  if check[x[1]]==0:
    L.append(-x[0])
    check[x[1]]=1
    if len(L2)==0:
      break
    z=L2.pop()
    p+=1
    ans.append(ans[-1]-(p-1)**2-x[0]-z+p**2)
  y-=1

print(max(ans))

Solution (Python):

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
bisect_left = bisect.bisect_left
bisect_right = bisect.bisect_right
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')


def A():
    a = LI()
    a.sort()
    print(a[0]*a[1]//2)  
    return


def B():
    d = defaultdict(int)
    s = II()
    def f(n):
        if n % 2:
            return 3 * n + 1
        return n // 2
    i = 1
    while not d[s]:
        d[s] = 1
        s = f(s)
        i += 1
    print(i)
    return


def C():
    n = II()
    h = LI()
    ans = h[0]
    for i in range(n - 1):
        ans += max(0, h[i + 1] - h[i])
    print(ans)
    return








def D():
    n, k = LI()
    ma = []
    for _ in range(n):
        t, di = LI()
        ma.append((di, t))
    ma.sort()
    ma = deque(ma)
    s = defaultdict(int)
    t = 0
    ans = 0
    q = []
    for _ in range(k):
        di,ti = ma.pop()
        ans += di
        heappush(q, (di, ti))
        if not s[ti]:
            t += 1
        s[ti] += 1
    ans += t ** 2
    ans = [ans]
    while ma and q:
        di, ti = ma.pop()
        while s[ti] and ma:
            di, ti = ma.pop()
        if not ma and s[ti]:
            break
        d1, t1 = heappop(q)
        while s[t1] == 1 and q:
            d1, t1 = heappop(q)
        if not q and s[t1] == 1:
            break
        s[t1] -= 1
        tmp = ans[-1]
        tmp = tmp - d1 + di - t ** 2
        t += 1
        tmp += t ** 2
        ans.append(tmp)
        heappush(q, (di, ti))
        s[ti] += 1
    print(max(ans))


    return


if __name__ == '__main__':
    D()

Solution (Python):
from collections import deque
n,k = map(int,input().split())
ans = 0
ansl = []
sushi = []
sushi1 = deque()
sushi2 = []
various = [0 for i in range(n)]
v = 0
for i in range(n):
    td = list(map(int,input().split()))
    sushi.append(td)
sushi.sort(key=lambda x:x[1],reverse=True)
for i in range(n):
    if i < k:
        ans += sushi[i][1]
        if various[sushi[i][0]-1] == 0:
            v += 1
        various[sushi[i][0]-1] += 1
        sushi1.append(sushi[i])
    else:
        sushi2.append(sushi[i])
ansl.append(ans+v*v)
for i in range(n-k):
    if various[sushi2[i][0]-1] == 0:
        key = 0
        while key < 1 and len(sushi1) > 0:
            a,b = sushi1.pop()
            if various[a-1] > 1:
                key += 1
                various[a-1] -= 1
        if key > 0:
            various[sushi2[i][0]-1] += 1
            ans = ans + sushi2[i][1] - b
            v += 1
            ansl.append(ans+v*v)
print(max(ansl))

Solution (Python):
import heapq

def main():
    N, K = map(int, input().split())
    sushi_list = []
    for _ in range(N):
        t, d = map(int, input().split())
        sushi_list.append((d,t))
    sushi_list = sorted(sushi_list, reverse=True)

    
    keep = []
    
    exchange = []
    
    types = set()
    for i in range(K):
        d, t = sushi_list[i]
        if t not in types:
            keep.append(d)
            types.add(t)
        else:
            heapq.heappush(exchange, d)

    base_point1 = sum(keep)
    base_point2 = sum(exchange)
    bonus_point = len(types)

    ans = base_point1 + base_point2 + bonus_point ** 2
    
    
    for i in range(K, N):
        if len(exchange) == 0:
            break

        d, t = sushi_list[i]
        
        if t in types:
            continue 
        types.add(t)
        
        base_point1 += d
        
        base_point2 -= heapq.heappop(exchange)
        bonus_point += 1
        ans = max(ans, base_point1 + base_point2 + bonus_point ** 2)

    print(ans)


    

main()

Solution (Python):
n, k = map(int, input().split())
sushi = [list(map(int, input().split())) for _ in range(n)]
sushi.sort(key=lambda x: x[1], reverse=True)

leaders = []
others = []

appeared = [False] * (n + 1)
for t, d in sushi:
    if appeared[t]:
        others.append(d)
    else:
        leaders.append(d)
        appeared[t] = True

def cumsum(a):
    res = [0] * (len(a) + 1)
    for i in range(len(a)):
        res[i + 1] = res[i] + a[i]
    return res

cumsum_leaders = cumsum(leaders)
cumsum_others = cumsum(others)

ans = 0
for i in range(min(k, len(leaders)), 0, -1):
    if k - i > len(others):
        break
    score = i ** 2 + cumsum_leaders[i] + cumsum_others[k - i]
    ans = max(ans, score)

print(ans)

Solution (Python):
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
import math
import bisect
import random
from itertools import permutations, accumulate, combinations, product
import sys
import string
from bisect import bisect_left, bisect_right
from math import factorial, ceil, floor
from operator import mul
from functools import reduce


INF = float('inf')
def LI(): return list(map(int, sys.stdin.readline().split()))
def I(): return int(sys.stdin.readline())
def LS(): return sys.stdin.readline().split()
def S(): return sys.stdin.readline().strip()
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def LSR(n): return [LS() for i in range(n)]
def SRL(n): return [list(S()) for i in range(n)]
def MSRL(n): return [[int(j) for j in list(S())] for i in range(n)]
mod = 1000000007


n, k = LI()
L = []
for kind, point in LIR(n):
    L += [(point, kind)]


L.sort()
que1 = deque(L[-k:])
que2 = deque(L[:-k])
ret = sum([point for point, kind in que1])
kind_cnt = Counter([i[1] for i in que1])
now_kinds = len(kind_cnt)
ans = ret + now_kinds ** 2
while que1:
    point1, kind1 = que1.popleft()
    if kind_cnt[kind1] > 1:
        kind_cnt[kind1] -= 1
        ret -= point1
        while que2:
            point2, kind2 = que2.pop()
            if not kind_cnt[kind2]:
                kind_cnt[kind2] += 1
                ret += point2
                now_kinds += 1
                ans = max(ans, ret + now_kinds ** 2)
                break
        else:
            break



print(ans)

Solution (Python):

n,k = map(int,input().split())
raw = [[] for _ in range(n)]
for _ in range(n):
  t,d = map(int,input().split())
  t -= 1
  raw[t].append(d)
only = []
other = []
for i in range(n):
  if len(raw[i]) != 0:
    raw[i].sort(reverse = True)
    only.append(raw[i][0])
    other += raw[i][1:]
only.sort(reverse = True)
only += [-10 ** 18 for _ in range(k)]
other.sort(reverse = True)
now = sum(only[:k])
can = [now + k * k]
for j in range(k):
  try:
    now -= only[k-1-j]
    now += other[j]
    can.append(now + (k-1-j) ** 2)
  except:
    break
print(max(can))

Solution (Python):

import heapq
import sys
input = sys.stdin.readline

def main():
	[N,K]=[int(x) for x in input().split()]
	td=[[int(x) for x in input().split()] for _ in range(N)]
	td.sort(key=lambda x:x[1],reverse=True)
	
	
	keep = []  
	exchange = []  
	types = set() 
	for i in range(K):
	    [t, d] = td[i]
	    if t not in types:
	        keep.append(d)
	        types.add(t)
	    else:
	        heapq.heappush(exchange, d)
	 
	basic_point_1 = sum(keep)
	basic_point_2 = sum(exchange)
	types_bonus = len(types)
	ans = basic_point_1 + basic_point_2 + types_bonus**2
	 
	
	for i in range(K, N):
	    if len(exchange) == 0:  
	        break
	    [t, d] = td[i]
	    if t in types:
	        continue
	    types.add(t)
	    basic_point_1 += d
	    basic_point_2 -= heapq.heappop(exchange) 
	    types_bonus += 1
	    ans = max(ans, basic_point_1 + basic_point_2 + types_bonus**2)
	print(ans)
        
if __name__ == "__main__":
  main()

Solution (Python):
import sys
import math
from collections import defaultdict

sys.setrecursionlimit(10**7)
def input():
    return sys.stdin.readline()[:-1]

mod = 10**9 + 7

def I(): return int(input())
def II(): return map(int, input().split())
def III(): return list(map(int, input().split()))
def Line(N):
    read_all = [tuple(map(int, input().split())) for _ in range(N)]
    return map(list,zip(*read_all))



from collections import deque

N,K = II()
t,d = Line(N)

x = []
for i in range(N):
    x.append([t[i],d[i]])

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

used = []
for i in range(K):
    used.append(x[i])

a = defaultdict(list)
for u in used:
    a[u[0]].append(u[1])

num = len(a.keys())

rem = []
for k in a.keys():
    if len(a[k])>=2:
        a[k].sort(reverse=True)
        for i in range(1,len(a[k])):
            rem.append(a[k][i])
rem.sort()
rem = deque(rem)

b = defaultdict(list)
for i in range(N):
    if a[t[i]]==[]:
        b[t[i]].append(d[i])

app = []
for k in b.keys():
    app.append(max(b[k]))
app.sort(reverse=True)
app = deque(app)

val = sum([used[i][1] for i in range(len(used))]) + num**2
temp = val
while (rem and app):
    re,ap = rem.popleft(), app.popleft()
    temp = temp-re+ap-num**2+(num+1)**2
    if val < temp:
        val = temp
    num += 1

print(val)

Solution (Python):
from heapq import heappop, heappush
N, K = map(int, input().split())
KMAX = 10 ** 5 + 1
TD = []
for _ in range(N):
    t, d = map(int, input().split())
    TD.append((d, t))

TD.sort(reverse=True)

pioneer = []
successor = []
appear = [False] * KMAX
cnt = 0
nsp = 0  
base = 0
best = []

for td in TD:
    d, t = td
    if cnt < K:
        heappush(successor if appear[t] else pioneer, (d, t))
        nsp += 0 if appear[t] else 1
        appear[t] = True
        base += d
        cnt += 1
        if cnt == K:
            heappush(best, -(base + nsp ** 2))
        continue
    if not successor:
        break
    if appear[t]:
        continue
    cd, ct = heappop(successor)
    appear[t] = True
    heappush(pioneer, (d, t))
    base += (d-cd)
    nsp += 1
    heappush(best, -(base + nsp ** 2))

print(-heappop(best))

Solution (Python):
N, K = map(int, input().split())
td = [list(map(int, input().split()))
      for _ in range(N)]
td.sort(key=lambda x: -x[1])
q = []
v = set()
sd = 0
for t, d in td[:K]:
    sd += d
    if t in v:
        q.append(d)
    v.add(t)
ans = len(v) ** 2 + sd
for t, d in td[K:]:
    if 0 >= len(q):
        break
    if t in v:
        continue
    v.add(t)
    md = q.pop()
    sd = sd - md + d
    tans = len(v) ** 2 + sd
    ans = max(ans, tans)
print(ans)

Solution (Python):
N, K = map(int, input().split())
td = [list(map(int, input().split()))
      for _ in range(N)]
td.sort(key=lambda x: -x[1])
q = []
v = set()
cnt = 0
for t, d in td[:K]:
    cnt += d
    if t in v:
        q.append(d)
    else:
        v.add(t)
cnt += len(v) ** 2
ans = cnt
for t, d in td[K:]:
    if t not in v and len(q) != 0:
        x = q.pop()
        cnt += d + 2 * len(v) + 1 - x
        v.add(t)
        ans = max(ans, cnt)
print(ans)

Solution (Python):
N, K = map(int, input().split())
td = sorted([list(map(int, input().split()))
             for _ in range(N)], key=lambda x: x[1], reverse=True)
q = []
v = set()
cnt = 0
for t, d in td[:K]:
    cnt += d
    if t in v:
        q.append(d)
    else:
        v.add(t)
cnt += len(v) ** 2
ans = cnt
for t, d in td[K:]:
    if t not in v and len(q) != 0:
        x = q.pop()
        cnt += d + 2 * len(v) + 1 - x
        v.add(t)
        ans = max(ans, cnt)
print(ans)

Solution (Python):
from heapq import heappop, heappush

N, K = map(int, input().split())
td = sorted([list(map(int, input().split()))
             for _ in range(N)], key=lambda x: x[1], reverse=True)
q = []
v = set()
cnt = 0
for t, d in td[:K]:
    cnt += d
    if t in v:
        heappush(q, d)
    else:
        v.add(t)
cnt += len(v) ** 2
ans = cnt
for t, d in td[K:]:
    if t not in v and len(q) != 0:
        x = heappop(q)
        cnt += d + 2 * len(v) + 1 - x
        v.add(t)
        ans = max(ans, cnt)
print(ans)

Solution (Python):
from heapq import heappop, heappush
n, k = map(int, input().split())
lst = [list(map(int, input().split())) for i in range(n)]
lst = sorted(lst, reverse=True, key=lambda x:x[1])
q = []
v = set()
cnt = 0
for t, d in lst[:k]:
    cnt += d
    if t in v:
        heappush(q, d)
    else:
        v.add(t)
cnt += len(v)**2
ans = cnt
for t, d in lst[k:]:
    if t not in v and len(q)!=0:
        x = heappop(q)
        cnt += d + 2*len(v) + 1 - x
        v.add(t)
        ans = max(ans, cnt)
print(ans)

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

N, K = map(int,input().split())
td = [list(map(int, input().split())) for _ in range(N)]
td.sort(key=lambda x: (x[0],x[1]),reverse=True)

x= []
y= []
y.append(td[0][1])
for i in range(1,N):
    if td[i][0] != td[i-1][0]:
        y.append(td[i][1])
    else:
        x.append(td[i][1])
x.sort(reverse=True)
y.sort(reverse=True)
ans = 0
sum_y = 0
sum_x = []
tmp = 0
sum_x.append(0)
for i in range(len(x)):
    tmp += x[i]
    sum_x.append(tmp)

for i in range(1,min(K,len(y))+1):
    sum_y += y[i-1]
    if len(sum_x) < K-i+1: continue
    ans = max(ans, sum_y + sum_x[K-i] + i*i)
    
print(ans)

Solution (Python):
n, m = [int(i) for i in input().split()]
td = [[int(i) for i in input().split()] for n in range(n)]
td.sort(key=lambda x:-x[1])
memo = set()
a = []
for t, d in td:
  if t in memo:
    a.append((d, 0))
  else:
    a.append((d, 1))
  memo.add(t)
a = [(-x, x, d) for x, d in a]
import heapq
heapq.heapify(a)
val = 0
kind = 0
b = []
for _ in range(m):
  ele = heapq.heappop(a)
  val += ele[1]
  kind += ele[2]
  if ele[2] == 0:
    b.append(ele[1])
ans = val + kind ** 2
while (len(a) > 0 and len(b)>0):
  val -= b.pop()
  flag = False
  while(len(a) > 0):
    elem = heapq.heappop(a)
    if elem[2] == 1:
      flag = True
      break
  if not flag:
    break
  val += elem[1]
  kind += 1
  tmpans = val + kind ** 2
  if tmpans > ans:
    ans = tmpans
print(ans)

Solution (Python):
n, k = map(int, input().split())
TD = [[] for i in range(n)]
for i in range(n):
  TD[i] = list(map(int, input().split()))
  
TD.sort(key = lambda x:x[1], reverse = True)

ans = 0
huku = []
su = set([])

for i, j in TD[:k]:
  ans += j
  if i in su:
    huku.append([i,j])
  su.add(i)
ans += len(su)**2
huku.sort(key = lambda x:x[1], reverse = True)

ansl = []
ansl.append(ans)
for i,j in TD[k:]:
  if i in su:
    continue
  elif huku == []:
    break
  else:
    temp = ansl[-1] + j - huku.pop()[1] + (len(su)+1)**2 -len(su)**2
    su.add(i)
    ansl.append(temp)

print(max(ansl))

Solution (Python):
from operator import itemgetter


n, k = map(int,input().split())
info = [list(map(int, input().split())) for i in range(n)]

info = sorted(info, key = itemgetter(1), reverse = True)

selected = info[0:k]
selected_only = []
selected_chohuku = []
unselected_only = []
memo = {}
for t, d in selected:
    if t not in memo:
        memo[t] = 1
        selected_only.append(d)
    else:
        selected_chohuku.append(d)

cnt_type = len(memo)
for t, d in info[k:]:
    if t not in memo:
        memo[t] = 1
        unselected_only.append(d)


sum_select = sum(selected_chohuku) + sum(selected_only) 
ans = cnt_type*cnt_type + sum_select

unselected_only = unselected_only[::-1]
for i in range(min(len(selected_chohuku), len(unselected_only))):
    cnt_type += 1
    sum_select += unselected_only[-1]
    sum_select -= selected_chohuku[-1]
    del unselected_only[-1]
    del selected_chohuku[-1]
    tmp = cnt_type*cnt_type + sum_select
    ans = max(ans, tmp)
print(ans)

Solution (Python):
from operator import itemgetter


n, k = map(int,input().split())
info = [list(map(int, input().split())) for i in range(n)]

info = sorted(info, key = itemgetter(1), reverse = True)

selected = info[0:k]
selected_only = []
selected_chohuku = []
unselected_only = []
memo = {}
for t, d in selected:
    if t not in memo:
        memo[t] = 1
        selected_only.append(d)
    else:
        selected_chohuku.append(d)

cnt_type = len(memo)
for t, d in info[k:]:
    if t not in memo:
        memo[t] = 1
        unselected_only.append(d)


sum_select = sum(selected_chohuku) + sum(selected_only) 
ans = cnt_type*cnt_type + sum_select

unselected_only = unselected_only[::-1]
for i in range(min(len(selected_chohuku), len(unselected_only))):
    cnt_type += 1
    sum_select += unselected_only[-1]
    sum_select -= selected_chohuku[-1]
    del unselected_only[-1]
    del selected_chohuku[-1]
    tmp = cnt_type*cnt_type + sum_select
    ans = max(ans, tmp)
print(ans)

Solution (Python):
mi = lambda: map(int, input().split())
n, k = mi()
sushis = [list(mi()) for _ in range(n)]
types = set()
sushis.sort(key = lambda x: x[1], reverse = True)
bp = tp = sp = 0
exts = []
for t, d in sushis[:k]:
    bp += d
    if t in types:
        exts += d,
    else:
        types.add(t)
        tp += 1
sp = bp+tp**2
for t, d in sushis[k:]:
    if not exts: break
    if t not in types:
        types.add(t)
        bp += d-exts.pop()
        tp += 1
        sp = max(sp, bp+tp**2)
print(sp)

Solution (Python):
mi = lambda: map(int, input().split())
n, k = mi()
sushis = [list(mi()) for _ in range(n)]
types = set()
sushis.sort(key = lambda x: x[1], reverse = True)
bp = tp = sp = 0
exts = []
for t, d in sushis[:k]:
    bp += d
    if t in types:
        exts += d,
    else:
        types.add(t)
        tp += 1
sp = bp+tp**2
for t, d in sushis[k:]:
    if not exts: break
    if t not in types:
        types.add(t)
        bp += d-exts.pop()
        tp += 1
        sp = max(sp, bp+tp**2)
print(sp)

Solution (Python):
import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians
from itertools import permutations, combinations, product
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect_left
from heapq import heappush, heappop

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()))
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
MOD = 10 ** 9 + 7

N, K = MAP()
td = [LIST() for _ in range(N)]
td.sort(key=lambda x:-x[1])

q = []
v = set()
s = 0
for t, d in td[:K]:
	s += d
	if t in v:
		heappush(q, d)
	else:  
		v.add(t)
s += len(v) ** 2  
ans = s

for t, d in td[K:]:  
	if t not in v and len(q) != 0:
		z = heappop(q)
		s += d + 2*len(v)+1-z  
		v.add(t)
		ans = max(ans, s)
print(ans)

Solution (Python):
n,k=map(int,input().split())
a=sorted([list(map(int,input().split()))for i in range(n)],key=lambda x:-x[1])
t=[0]*(n+1)
p,q=0,0
for i in a[:k]:
    p+=i[1]
    if t[i[0]]==0:
        q+=1
    t[i[0]]+=1
s=0
d=p+q*q
c=a[:k][::-1]
for i in a[k:]:
    if t[i[0]]==0:
        while s!=k:
            if t[c[s][0]]==1:
                s+=1
            else:
                break
        if s==k:
            break
        else:
            t[i[0]]+=1
            p-=c[s][1]-i[1]
            q+=1
            d=max(d,p+q*q)
            s+=1
print(d)

Solution (Python):
import heapq

N,K = map(int,input().split())

ans = 0

dt = []
maxt = 0

for i in range(N):

    t,d = map(int,input().split())

    dt.append([d,t])

    maxt = max(maxt,t)

dt.sort()
dt.reverse()

nsum = 0
nx = 0
uflag = [0] * (maxt+1)
up2mins = []
amari = []

for i in range(N):

    nt = dt[i][1]
    nd = dt[i][0]

    if i < K:

        nsum += nd

        if uflag[nt] == 0:
            uflag[nt] += 1
            nx += 1

        else:
            heapq.heappush(up2mins,nd)

    else:

        if uflag[nt] == 0:
            heapq.heappush(amari,-1 * nd)
            uflag[nt] += 1

ans = nsum + nx ** 2



for i in range(N-K+1):

    if len(amari) == 0 or len(up2mins) == 0:
        break

    mnd = heapq.heappop(up2mins)

    pnd = -1 * heapq.heappop(amari)

    nx += 1

    nsum = nsum - mnd + pnd

    ans = max(ans , nsum + nx ** 2)


print (ans)

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

n,k=map(int,input().split())
sushi=[list(map(int,input().split())) for _ in range(n)]
sushi.sort(key=lambda x:x[1],reverse=True)

from collections import Counter
sel=Counter()
ans=0
sta=[]

for t,d in sushi[:k]:
    ans+=d
    sel[t]+=1
    sta.append([t,d])

ans+=len(sel)**2
tmp=ans
for t,d in sushi[k:]:
    if t in sel:continue
    while sta:
        tt,dd=sta.pop()
        if sel[tt]>1:
            tmp+=d-dd+2*len(sel)+1
            ans=max(ans,tmp)
            sel[tt]-=1
            sel[t]+=1
            break
print(ans)

Solution (Python):
N, K = map(int, input().split())
dts = []
for _ in range(N):
    t, d = map(int, input().split())
    dts.append((d, t-1))

dts.sort(reverse=True)

tops = []
rests = []
isFounds = [False] * N
for d, t in dts:
    if isFounds[t]:
        rests.append(d)
    else:
        tops.append(d)
        isFounds[t] = True

tops.sort(reverse=True)
rests.sort(reverse=True)

xFr = max(1, K-len(rests))
xTo = min(K, len(tops))
iTop = xFr
iRest = K-xFr
sumD = sum(tops[:iTop]) + sum(rests[:iRest])
ans = sumD + xFr**2
for x in range(xFr+1, xTo+1):
    iRest -= 1
    sumD += tops[iTop] - rests[iRest]
    score = sumD + x**2
    ans = max(ans, score)
    iTop += 1

print(ans)

Solution (Python):
from heapq import heapify, heappush, heappop

N, K = map(int, input().split())
dts = []
for _ in range(N):
    t, d = map(int, input().split())
    dts.append((d, t-1))

dts.sort(reverse=True)

PQRem = []
isFounds = [False] * N
sumD = 0
for d, t in dts[:K]:
    sumD += d
    if isFounds[t]:
        heappush(PQRem, d)
    isFounds[t] = True
numKind = isFounds.count(True)

PQAdd = []
for d, t in dts[K:]:
    if not isFounds[t]:
        heappush(PQAdd, -d)
    isFounds[t] = True

ans = sumD + numKind**2
for x in range(numKind+1, K+1):
    if not PQRem or not PQAdd:
        break
    dRem = heappop(PQRem)
    dAdd = -heappop(PQAdd)
    sumD += -dRem + dAdd
    score = sumD + x**2
    ans = max(ans, score)

print(ans)

Solution (Python):
import heapq

N, K = map(int, input().split())
sushi = []

for _ in range(N):
    t, d = map(int, input().split())
    sushi.append((t, d))
sushi = sorted(sushi, key=lambda x: -x[1])

d_sushi = []  
heapq.heapify(d_sushi)  

fp = 0
tp = set()

for i in range(K):
    fp += sushi[i][1]
    if sushi[i][0] in tp:
        heapq.heappush(d_sushi, sushi[i][1])
    else:
        tp.add(sushi[i][0])
ans = fp+len(tp)**2

if N == K:
    print(ans)
    exit()

j = K
while d_sushi and len(tp) <= N:
    while sushi[j][0] in tp:
        j += 1
        if j == N:
            print(ans)
            exit()
    fp = fp-heapq.heappop(d_sushi)+sushi[j][1]
    tp.add(sushi[j][0])
    ans = max(ans, fp+len(tp)**2)

print(ans)

Solution (Python):


import heapq

def resolve():
    n, k = map(int, input().split())
    td = []

    
    for _ in range(n):
        t, d = map(int, input().split())
        heapq.heappush(td, (-d, t))

    score = 0
    types = set()
    discard = []

    for _ in range(k):
        d, t = heapq.heappop(td)  
        score -= d
        if t not in types:
            types.add(t)
        else:
            
            heapq.heappush(discard, (-d, t))

    ans = score + len(types)**2

    while td and discard:
        d, t = heapq.heappop(td)  

        if t in types:
            
            continue

        types.add(t)
        score -= d

        
        _d, _t = heapq.heappop(discard)  
        score -= _d

        ans = max(ans, score + len(types)**2)

    print(ans)

if __name__ == "__main__":
    resolve()

Solution (Python):
from operator import itemgetter

N, K = map(int, input().split())
TD = [list(map(int, input().split())) for _ in range(N)]

TD.sort(key=itemgetter(1), reverse=True)

remain = []
removable = []
used = [False for _ in range(N+1)]
val = 0
S = 0
for i, (t, d) in enumerate(TD):
    if i < K:
        S += d
        if not used[t]:
            val += 1
        else:
            removable.append(d)
        used[t] = True
    else:
        if not used[t]:
            remain.append(d)
            used[t] = True

S += val**2
removable.sort()

delta = 0
ans = S
for k, r in enumerate(remain):
    if k >= len(removable):
        break
    val += 1
    delta += r - removable[k] + 2*val - 1
    ans = max(ans, S+delta)
print(ans)

Solution (Python):

import sys, math, fractions, itertools, heapq

def solve(N: int, k: int, t: "List[int]", d: "List[int]"):
    arr = sorted(zip(t, d), key=lambda x: x[1], reverse=True)
    q = [] 
    v = set() 
    s = 0 
    for t,d in arr[:k]:
        s += d
        if t in v:
            heapq.heappush(q,d)
        else:
            v.add(t)
    s += len(v)**2
    ans = s 
    for t,d in arr[k:]: 
        if t not in v and len(q)!=0: 
            z = heapq.heappop(q) 
            s += d + 2*len(v) + 1 - z 
            v.add(t)
            ans=max(ans,s) 
    print(ans)
    return



def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  
    K = int(next(tokens))  
    t = [int()] * (N)  
    d = [int()] * (N)  
    for i in range(N):
        t[i] = int(next(tokens))
        d[i] = int(next(tokens))
    solve(N, K, t, d)

if __name__ == '__main__':
    main()

Solution (Python):
import heapq
n,k = (int(x) for x in input().split())
arr = []
discard = []
type = set()
score = 0

for i in range(n):
  a,b = (int(x) for x in input().split())
  heapq.heappush(arr, (-b, a))
  

for i in range(k):
  d, t = heapq.heappop(arr)
  score -= d
  if t not in type:
    type.add(t)
  else:
    heapq.heappush(discard, (-d, t))

bonus = len(type)
ans = score + bonus**2

while arr and discard:
  pd, pt = heapq.heappop(arr)  
  if pt not in type:
    _pd, _pt = heapq.heappop(discard) 
    type.add(pt)
    score = score - _pd - pd
    bonus += 1
    tmp = score + bonus**2
    ans = max(ans, tmp)
    
print(ans)

Solution (Python):
from heapq import heappush, heappop
N, K = map(int, input().split())
TD = [list(map(int, input().split())) for _ in range(N)]
TD.sort(key=lambda x:x[1], reverse=True)
muptiple = set()
for i in range(len(TD)):
    flg = 0
    if TD[i][0] not in muptiple:
        muptiple.add(TD[i][0])
        flg = 1
    TD[i][0] = flg
TD.reverse()
ret = []
point = 0
vari = 0
total = 0
for i in range(K):
    v = TD.pop()
    vari += v[0]
    point += v[1]
    if not v[0]:
        heappush(ret, v[1])

total = vari ** 2 + point

while len(TD) > 0 and len(ret) > 0:
    v = TD.pop()
    if v[0] == 0:
        continue
    pre_t = heappop(ret)
    point -= pre_t - v[1]
    vari += 1
    tmp = vari ** 2 + point
    total = max(total, tmp)

print(total)