Gluttony

AtCoder

IDabc144_e

Time2000ms

Memory256MB

Difficulty—

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: $N$ $K$ $A_1$ $A_2$ $...$ $A_N$ $F_1$ $F_2$ $...$ $F_N$ [samples]

Samples

Input #1

3 5
4 2 1
2 3 1

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 $2$.

Input #2

3 8
4 2 1
2 3 1

Output #2

0

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

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

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Gluttony",
    "description": {
      "content": "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 _co",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc144_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "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 _co...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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