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 Rust (1.42.0) (judge verdict: Accepted)

#[allow(dead_code)]
fn main() {
    let stdin = stdin();
    solve(StdinReader::new(stdin.lock()));
}

pub fn solve<R: BufRead>(mut reader: StdinReader<R>) {
    let (n, k) = reader.u2();
    let mut a = reader.uv(n);
    let mut f = reader.uv(n);
    a.sort();
    f.sort();
    f.reverse();

    let mut ng = -1isize;
    let mut ok = 1_000_000_000_000_000_001isize;
    while (ok - ng).abs() > 1 {
        let mid = (ok + ng) / 2;
        if is_ok(&a, &f, k, mid) {
            ok = mid
        } else {
            ng = mid
        }
    }
    println!("{}", ok);
}

fn is_ok(a: &Vec<usize>, f: &Vec<usize>, k: usize, mid: isize) -> bool {
    let mut over = 0;
    for i in 0..a.len() {
        if a[i] * f[i] > mid as usize {
            over += a[i] - mid as usize / f[i];
        }
    }
    over <= k
}

#[allow(unused_imports)]
use itertools::Itertools;
#[allow(unused_imports)]
use std::{cmp::*, collections::*, io::*, num::*, str::*};
#[allow(unused_imports)]
use stdin_reader::StdinReader;

#[allow(dead_code)]
pub mod stdin_reader {
    use std::{fmt::Debug, io::*, str::*};

    pub struct StdinReader<R: BufRead> {
        reader: R,
        buf: Vec<u8>,
        // Should never be empty
        pos: usize, // Should never be out of bounds as long as the input ends with '\n'
    }

    impl<R: BufRead> StdinReader<R> {
        pub fn new(reader: R) -> StdinReader<R> {
            let (buf, pos) = (Vec::new(), 0);
            StdinReader { reader, buf, pos }
        }

        pub fn n<T: FromStr>(&mut self) -> T
        where
            T::Err: Debug,
        {
            if self.buf.is_empty() {
                self._read_next_line();
            }
            let mut start = None;
            while self.pos != self.buf.len() {
                match (self.buf[self.pos], start.is_some()) {
                    (b' ', true) | (b'\n', true) => break,
                    (_, true) | (b' ', false) => self.pos += 1,
                    (b'\n', false) => self._read_next_line(),
                    (_, false) => start = Some(self.pos),
                }
            }
            match start {
                Some(s) => from_utf8(&self.buf[s..self.pos]).unwrap().parse().unwrap(),
                None => panic!("入力された数を超えた読み込みが発生しています"),
            }
        }

        fn _read_next_line(&mut self) {
            self.pos = 0;
            self.buf.clear();
            if self.reader.read_until(b'\n', &mut self.buf).unwrap() == 0 {
                panic!("Reached EOF");
            }
        }

        pub fn str(&mut self) -> String {
            self.n()
        }
        pub fn s(&mut self) -> Vec<char> {
            self.n::<String>().chars().collect()
        }
        pub fn i(&mut self) -> i64 {
            self.n()
        }
        pub fn i2(&mut self) -> (i64, i64) {
            (self.n(), self.n())
        }
        pub fn i3(&mut self) -> (i64, i64, i64) {
            (self.n(), self.n(), self.n())
        }
        pub fn u(&mut self) -> usize {
            self.n()
        }
        pub fn u2(&mut self) -> (usize, usize) {
            (self.n(), self.n())
        }
        pub fn u3(&mut self) -> (usize, usize, usize) {
            (self.n(), self.n(), self.n())
        }
        pub fn u4(&mut self) -> (usize, usize, usize, usize) {
            (self.n(), self.n(), self.n(), self.n())
        }
        pub fn u5(&mut self) -> (usize, usize, usize, usize, usize) {
            (self.n(), self.n(), self.n(), self.n(), self.n())
        }
        pub fn u6(&mut self) -> (usize, usize, usize, usize, usize, usize) {
            (self.n(), self.n(), self.n(), self.n(), self.n(), self.n())
        }
        pub fn f(&mut self) -> f64 {
            self.n()
        }
        pub fn f2(&mut self) -> (f64, f64) {
            (self.n(), self.n())
        }
        pub fn c(&mut self) -> char {
            self.n::<String>().pop().unwrap()
        }
        pub fn iv(&mut self, n: usize) -> Vec<i64> {
            (0..n).map(|_| self.i()).collect()
        }
        pub fn iv2(&mut self, n: usize) -> Vec<(i64, i64)> {
            (0..n).map(|_| self.i2()).collect()
        }
        pub fn iv3(&mut self, n: usize) -> Vec<(i64, i64, i64)> {
            (0..n).map(|_| self.i3()).collect()
        }
        pub fn uv(&mut self, n: usize) -> Vec<usize> {
            (0..n).map(|_| self.u()).collect()
        }
        pub fn uv2(&mut self, n: usize) -> Vec<(usize, usize)> {
            (0..n).map(|_| self.u2()).collect()
        }
        pub fn uv3(&mut self, n: usize) -> Vec<(usize, usize, usize)> {
            (0..n).map(|_| self.u3()).collect()
        }
        pub fn uv4(&mut self, n: usize) -> Vec<(usize, usize, usize, usize)> {
            (0..n).map(|_| self.u4()).collect()
        }
        pub fn fv(&mut self, n: usize) -> Vec<f64> {
            (0..n).map(|_| self.f()).collect()
        }
        pub fn cmap(&mut self, h: usize) -> Vec<Vec<char>> {
            (0..h).map(|_| self.s()).collect()
        }
    }
}