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: Time Limit Exceeded)

import sys
sys.setrecursionlimit(10**7)
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x) - 1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def II(): return int(sys.stdin.readline())
def SI(): return sys.stdin.readline().strip()
INF = 10 ** 18
MOD = 10 ** 9 + 7

debug = True
debug = False

def dprint(*objects):
    if debug == True:
        print(*objects)

def solve():
    N, K = LI()
    a_list = LI()
    f_list = LI()

    # 答えで二分探索

    low = 0
    high = (10**6)*(10**6)*2*(10**5)

    # 妥当な割り当て
    a_list = sorted(a_list)
    f_list = sorted(f_list, reverse=True)
    import math

    dprint(a_list)
    dprint(f_list)

    def judge(ans):
        # ans を答えにできるか
        cnt = 0
        for i in range(N):
            a = a_list[i]
            f = f_list[i]
            if a*f > ans:
                # 差分を訓練で埋める
                ki = math.ceil((a*f - ans) / f)
                cnt += ki
                if cnt > K:
                    dprint('False', ans, cnt)
                    return False
        dprint('True', ans, cnt)
        return True

    while low < high:
        mid = math.floor((low + high) / 2)

        guess = judge(mid)
        # dprint(high, low, mid, guess)

        if guess == True:
            # できるので、これより1少ないのが最大
            high = mid
        else:
            # できないので、これより大きい
            low = mid + 1
        # dprint(high, low)
    print(low)


solve()