Problem:
Score: 500 points

Problem Statement

Takahashi will take part in an eating contest. Teams of N members will compete in this contest, and Takahashi's team consists of N players numbered 1 through N from youngest to oldest. The consumption coefficient of Member i is A_i.

In the contest, N foods numbered 1 through N will be presented, and the difficulty of Food i is F_i. The details of the contest are as follows:

A team should assign one member to each food, and should not assign the same member to multiple foods.

It will take x \times y seconds for a member to finish the food, where x is the consumption coefficient of the member and y is the difficulty of the dish.

The score of a team is the longest time it takes for an individual member to finish the food.

Before the contest, Takahashi's team decided to do some training. In one set of training, a member can reduce his/her consumption coefficient by 1, as long as it does not go below 0. However, for financial reasons, the N members can do at most K sets of training in total.

What is the minimum possible score of the team, achieved by choosing the amounts of members' training and allocating the dishes optimally?

Constraints

All values in input are integers.

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

0 \leq K \leq 10^{18}

1 \leq A_i \leq 10^6\ (1 \leq i \leq N)

1 \leq F_i \leq 10^6\ (1 \leq i \leq N)

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 ... A_N
F_1 F_2 ... F_N

Output

Print the minimum possible score of the team.

Sample Input 1

3 5
4 2 1
2 3 1

Sample Output 1

2

They can achieve the score of 2, as follows:

Member 1 does 4 sets of training and eats Food 2 in (4-4) \times 3 = 0 seconds.

Member 2 does 1 set of training and eats Food 3 in (2-1) \times 1 = 1 second.

Member 3 does 0 sets of training and eats Food 1 in (1-0) \times 2 = 2 seconds.

They cannot achieve a score of less than 2, so the answer is 2.

Sample Input 2

3 8
4 2 1
2 3 1

Sample Output 2

0

They can choose not to do exactly K sets of training.

Sample Input 3

11 14
3 1 4 1 5 9 2 6 5 3 5
8 9 7 9 3 2 3 8 4 6 2

Sample Output 3

12

Solution in Python (3.4.3) (judge verdict: Runtime Error)

N, K = map(int, input().split())
A = list(map(int, input().split()))
F = list(map(int, input().split()))

##　Aは昇順Fは降順に並び替える
A.sort() 
F.sort(reverse = True)

##　成績(A × F)の目標をxにしたときに何回修行が必要かを求める関数
def target(x):
    train_count = 0
    for i in range(N):
        a = A[i]
        targ_a = x // F[i] #目標を達成した時の消費コストA
        if targ_a < a:
            train_count = train_count + a - targ_a 
    return train_count <= K　#ただし合計がKを超えないもの

##　二分探索(リストを半分ずつ削って達成可能な目標を探す)
left = -1                        #一番左
right = A[-1] * F[0]             #一番右(Aの最大値 × Fの最大値)
while right > left + 1:          #一番右が一番左より大きい間（一致したら終了）
    middle = (left + right) // 2 #真ん中
    if target(middle):           #目標を真ん中にして達成可能なら
        right = middle           #一番右を真ん中にする（残りの右側は無駄に時間かかってるから切り捨てる）
    
    else:                        #達成できないなら(K回を超えてしまうとき）
        left = middle            #一番左を真ん中にする（残りの左側は達成不可だから切り捨てる）

print(right)