Problem:
 Score : 800 points    Problem Statement Takahashi and Aoki will take N exams numbered 1 to N .
They have decided to compete in these exams.
The winner will be determined as follows:    For each exam i , Takahashi decides its importance  c_i , which must be an integer between l_i and u_i (inclusive).    Let A be \sum_{i=1}^{N} c_i \times (Takahashi's score on Exam i ), and B be \sum_{i=1}^{N} c_i \times (Aoki's score on Exam i ). Takahashi wins if A \geq B , and Aoki wins if A < B .    Takahashi knows that Aoki will score b_i on Exam i , with his supernatural power.  Takahashi himself, on the other hand, will score 0 on all the exams without studying more. For each hour of study, he can increase his score on some exam by 1 . (He can only study for an integer number of hours.)
However, he cannot score more than X on an exam , since the perfect score for all the exams is X .  Print the minimum number of study hours required for Takahashi to win.      Constraints  1 \leq N \leq 10^5  1 \leq X \leq 10^5  0 \leq b_i \leq X  (1 \leq i \leq N)  1 \leq l_i \leq u_i \leq 10^5  (1 \leq i \leq N)  All values in input are integers.         Input Input is given from Standard Input in the following format:  N  X  b_1  l_1  u_1  b_2  l_2  u_2  :  b_N  l_N  u_N       Output Print the minimum number of study hours required for Takahashi to win.        Sample Input 1 2 100
85 2 3
60 1 1      Sample Output 1 115  One optimal strategy is as follows:    Choose c_1 = 3, c_2 = 1 .    Study to score 100 on Exam 1 and 15 on Exam 2 .    Then, A = 3 \times 100 + 1 \times 15 = 315 , B = 3 \times 85 + 1 \times 60 = 315 and Takahashi will win.       Sample Input 2 2 100
85 2 3
60 10 10      Sample Output 2 77       Sample Input 3 1 100000
31415 2718 2818      Sample Output 3 31415       Sample Input 4 10 1000
451 4593 6263
324 310 6991
378 1431 7068
71 1757 9218
204 3676 4328
840 6221 9080
684 1545 8511
709 5467 8674
862 6504 9835
283 4965 9980      Sample Output 4 2540

Solution (Python):
import sys
N, X = map(int, input().split())
BLU = [tuple(map(int, sys.stdin.readline().split())) for _ in range(N)]
B, L, U = map(list, zip(*BLU))
C = [(u-l)*b for b, l, u in BLU]
D = [(X*u - c, u, c, l, b) for u, c, l, b in zip(U, C, L, B)]
D.sort(reverse = True)
SL = sum(l*b for l, b in zip(L, B))
SS = 0
for i, (d, _, _, _, _) in enumerate(D):
    SS += d
    if SS >= SL:
        break
SSb = SS - d
lans = i*X
m = 10**10
for d, u, c, l, b in D[:i]:
    m = min(m, -(-(c + SL - (SS - d))//u), -(((SS - d) - SL)//l))
    
for _, u, c, l, b in D[i:]:
    m = min(m, -(-(c + SL - SSb)//u), -((SSb - SL)//l))
lans += m

ans = (i+1) * X
m = 0
for _, u, _, _, _ in D[:i+1]:
    m = max(m, (SS - SL)//u)
print(min(lans, ans - m))

Solution (Python):
from operator import itemgetter
N, X = map(int, input().split())
S = [list(map(int, input().split())) for i in range(N)]
A = []
aoki = 0
for i, (b, l, u) in enumerate(S):
    A.append([(X-b)*u + (b)*l, i])
    aoki += b*l
A.sort(reverse=True, key=itemgetter(0))
ans = 0
tak = 0
for iaaaa, (a, i) in enumerate(A):
    if aoki >= a:
        aoki -= a
        ans += X
        if aoki==0:
            print(ans)
            exit()
    else:
        break
mi = float("inf")
aoki_ = aoki
for j in range(iaaaa, N):
    a, i = A[j]
    b, l, u = S[i]
    aoki = aoki_
    an, m = divmod(aoki, l)
    if m!=0:
        an += 1
    mi = min(mi, an)
    aoki += (u-l) * b
    an, m = divmod(aoki, u)
    if m!=0:
        an += 1
    mi = min(mi, an)
ans_ = ans + mi

a, i = A[iaaaa]
aoki_ -= a

anss = (iaaaa)*X
mi = float("inf")
for a, i in A[:iaaaa]:
    b, l, u = S[i]
    aoki = aoki_ + a
    an, m = divmod(aoki, l)
    if m!=0:
        an += 1
    mi = min(mi, an)
    aoki += (u-l) * b
    an, m = divmod(aoki, u)
    if m!=0:
        an += 1
    mi = min(mi, an)

print(min(ans_, anss+mi))

Solution (Python):
N,X = list(map(int,input().split()))

data = []
l_sum=0
for i in range(N):
    b,l,u = list(map(int,input().split()))
    data.append([b,l,u,(X-b)*u+b*l])
    l_sum+=b*l

if l_sum==0:
    print(0)
else:
    data=sorted(data,key=lambda x:x[3],reverse=True)
    
    S=[-l_sum]
    s=-l_sum
    for i in range(N):
        s += data[i][3]
        S.append(s)
    
    def judge(P):
    
        n=P//X
        p=P%X
    
        if S[n]>=0:
            return True
        else:
            new_list = []
            for i in range(N):
                if i>=n:
                    b,l,u,x = data[i]
                    if p>=b:
                        new_list.append(u*(p-b)+l*b)
                    else:
                        new_list.append(l*p)
                else:
                    b,l,u,x = data[i]
                    new_list.append(max(u*(p-X),l*p-u*X+b*(u-l))+data[n][3])
                    
            if S[n] + max(new_list)>=0:
                return True
            else:
                return False
    
    max_P=N*X
    
    def bisect(m,M):
        if M-m==1:
            return M
        else:
            if judge((m+M)//2):
                return bisect(m,(m+M)//2)
            else:
                return bisect((m+M)//2,M)
    
    print(bisect(0,max_P))