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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
import java.io.*;
import java.util.function.*;
// import lib.util.*;
// import lib.graph.*;
// import lib.io.*;
// import lib.math.*;

public class Main {

    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);
        int N = sc.nextInt();
        long K = sc.nextLong();
        int[] A = new int[N];
        Integer[] F = new Integer[N];
        for (int i = 0; i < N; i++) {
            A[i] = sc.nextInt();
        }
        for (int i = 0; i < N; i++) {
            F[i] = sc.nextInt();
        }
        Arrays.sort(A);
        Arrays.sort(F, Comparator.reverseOrder());
        long l = -1;
        long r = 1_000_000_000_001L;
        while (r - l > 1) {
            long mid = (l + r) / 2;
            long tmp = K;
            for (int i = 0; i < N; i++) {
                tmp -= A[i] - Math.ceil(mid / F[i]);
            }
            if (tmp >= 0) {
                r = mid;
            } else {
                l = mid;
            }
        }

        out.println(r);

        out.flush();
    }

}

class UnionFindTree {
    int[] root;
    int[] rank;
    int[] size;
    int m;

    public UnionFindTree(int n) {
        this.root = new int[n];
        this.rank = new int[n];
        this.size = new int[n];
        this.m = n;
        for (int i = 0; i < n; i++) {
            root[i] = i;
            size[i] = 1;
        }
    }

    public int find(int x) {
        if (root[x] == x)
            return x;
        else {
            return root[x] = find(root[x]);
        }
    }

    public void unite(int x, int y) {
        x = find(x);
        y = find(y);
        if (x == y)
            return;
        if (rank[x] < rank[y]) {
            size[find(y)] = size[find(x)];
            root[x] = y;
        } else {
            size[find(x)] = size[find(y)];
            root[y] = x;
            if (rank[x] == rank[y])
                rank[x]++;
        }
        m--;
    }

    public boolean same(int x, int y) {
        return find(x) == find(y);
    }

    public int size(int i) {
        return this.size[find(i)];
    }
}

class Dijkstra {
    private static int prev[];
    private static long dist[];

    public Dijkstra(AbstractGraph graph, int s) {
        prev = new int[graph.n];
        dist = new long[graph.n];
        Arrays.fill(prev, -1);
        Arrays.fill(dist, Long.MAX_VALUE);
        PriorityQueue<Integer> searching = new PriorityQueue<>((x, y) -> Long.compare(dist[x], dist[y]));
        dist[s] = 0;
        searching.add(s);
        while (searching.size() > 0) {
            int now = searching.poll();
            for (Edge e : graph.getEdges(now)) {
                int next = e.to;
                long c = e.cost;
                if (dist[now] + c < dist[next]) {
                    dist[next] = dist[now] + c;
                    prev[next] = now;
                    searching.add(next);
                }
            }
        }
    }

    public int[] path(int to) {
        ArrayList<Integer> rev = new ArrayList<>();
        for (int now = to; now != -1; now = this.prev[now]) {
            rev.add(now);
        }
        int[] path = new int[rev.size()];
        for (int i = 0; i < path.length; i++) {
            path[i] = rev.get(path.length - i - 1);
        }
        return path;
    }
}

class WF {
    private static long[][] dist;

    public WF(AbstractGraph graph) {
        dist = new long[graph.n][graph.n];
        for (int i = 0; i < dist.length; i++) {
            Arrays.fill(dist[i], Integer.MAX_VALUE);
        }
        for (int i = 0; i < graph.n; i++) {
            for (Edge e : graph.getEdges(i)) {
                dist[i][e.to] = e.cost;
            }
            dist[i][i] = 0;
        }
        for (int k = 0; k < graph.n; k++) {
            for (int i = 0; i < graph.n; i++) {
                for (int j = 0; j < graph.n; j++) {
                    if (dist[i][k] != Integer.MAX_VALUE && dist[k][j] != Integer.MAX_VALUE) {
                        dist[i][j] = Math.min(dist[i][j], dist[i][k] + dist[k][j]);
                    }
                }
            }
        }
    }

    public static long getShortest(int s, int t) {
        return dist[s][t];
    }

    public static long[][] getAllDist() {
        return dist;
    }

    public static boolean isNegativeLoop() {
        for (int i = 0; i < dist.length; i++) {
            if (dist[i][i] < 0) {
                return true;
            }
        }
        return false;
    }
}

class Edge {
    int from, to;
    long cost;

    public Edge(int from, int to, long cost) {
        this.from = from;
        this.to = to;
        this.cost = cost;
    }

    public Edge(int from, int to) {
        this.from = from;
        this.to = to;
        this.cost = 1;
    }

    public Edge reverse() {
        return new Edge(to, from, cost);
    }
}

@SuppressWarnings("unchecked")
abstract class AbstractGraph {
    int n;
    int m;
    ArrayList<Edge>[] edges;

    public AbstractGraph(int n) {
        this.n = n;
        this.m = 0;
        this.edges = new ArrayList[n];
        for (int i = 0; i < n; i++) {
            this.edges[i] = new ArrayList<Edge>();
        }
    }

    public void addEdge(Edge e) {
        this.m++;
        this.edges[e.from].add(e);
    }

    public int getV() {
        return this.n;
    }

    public int getE() {
        return this.m;
    }

    public ArrayList<Edge> getEdges(int v) {
        return this.edges[v];
    }

    abstract public boolean isBipartite();

    public boolean isTree() {
        // require Modifying.
        return false;
    }
}

class Graph extends AbstractGraph {
    int n;
    int m;
    // array of edges which is connect to the node
    ArrayList<Edge>[] edges;

    public Graph(int n) {
        super(n);
    }

    public void addEdge(int from, int to, int cost) {
        Edge e = new Edge(from, to, cost);
        super.addEdge(e);
        super.addEdge(e.reverse());
        this.m++;
    }

    @Override
    public void addEdge(Edge e) {
        this.edges[e.from].add(e);
        this.edges[e.to].add(e.reverse());
        this.m++;
    }

    public int getV(int v) {
        return n;
    }

    public int getE() {
        return m;
    }

    public boolean isBipartite() {
        int[] color = new int[n];
        PriorityQueue<Integer> queue = new PriorityQueue<>();
        HashSet<Integer> visited = new HashSet<>();
        queue.add(0);
        color[0] = 1;
        while (queue.size() > 0) {
            int now = queue.poll();
            visited.add(now);
            for (Edge e : getEdges(now)) {
                if (visited.contains(e.to)) {
                    continue;
                }
                if (color[e.to] == color[now])
                    return false;
                queue.add(e.to);
                if (color[e.to] == 0)
                    color[e.to] = -1 * color[now];
            }
        }
        return true;
    }
}

class DirectedGraph extends AbstractGraph {
    int n;
    int m;
    // array of edges which is connect to the node
    ArrayList<Edge>[] edges;

    public DirectedGraph(int n) {
        super(n);
    }

    public void addEdge(int from, int to, int cost) {
        Edge e = new Edge(from, to, cost);
        super.addEdge(e);
        this.m++;
    }

    @Override
    public void addEdge(Edge e) {
        this.edges[e.from].add(e);
        this.m++;
    }

    public int getV(int v) {
        return this.n;
    }

    public int getE() {
        return this.m;
    }

    public boolean isBipartite() {
        // need to rewrite to work
        return false;
    }

}

class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        } else {
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }

    private int readByte() {
        if (hasNextByte())
            return buffer[ptr++];
        else
            return -1;
    }

    private static boolean isPrintableChar(int c) {
        return 33 <= c && c <= 126;
    }

    public boolean hasNext() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr]))
            ptr++;
        return hasNextByte();
    }

    public String next() {
        if (!hasNext())
            throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    public long nextLong() {
        if (!hasNext())
            throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while (true) {
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            } else if (b == -1 || !isPrintableChar(b)) {
                return minus ? -n : n;
            } else {
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }

    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
            throw new NumberFormatException();
        return (int) nl;
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }
}

class MyMath {
    public static long gcm(long a, long b) {

        // if (a < b)
        // return gcm(b, a);

        // if (b == 0 || a % b == 0)
        // return b;

        // return gcm(b, a % b);
        if (a < b) {
            long tmp = a;
            a = b;
            b = tmp;
        }
        long r = -1;
        while (r != 0) {
            r = a % b;
            a = b;
            b = r;
        }
        return a;
    }

    public static long summation(long a, long b) {
        return b * (b + 1) / 2 - a * (a - 1) / 2;
    }

    public static long factorial(long n) {

        if (n <= 1)
            return 1;
        else
            return factorial(n - 1) * n;
    }

    public static long[][] binomialTable(int a, long m) {
        long[][] table = new long[a + 1][a + 1];
        for (int i = 0; i < a + 1; i++) {
            table[0][a] = 0;
            table[i][0] = 1;
            table[i][i] = 1;
        }
        for (int i = 1; i < a + 1; i++) {
            for (int j = 1; j < a + 1; j++) {
                if (i < j)
                    table[i][j] = 0;
                else {
                    table[i][j] = (table[i - 1][j - 1] + table[i - 1][j]) % m;
                }
            }
        }
        return table;
    }

    public static long binomial(int n, int k, long m) {
        long res = 1;
        for (int l = n - k + 1; l <= n; l++) {
            res = (res % m) * (l % m) % m;
        }
        for (int r = 1; r <= k; r++) {
            res = (res % m) * modinv(r, m) % m;
        }
        return res;
    }

    public static long repeatSquarePow(long a, long n, long p) {
        if (n == 0)
            return 1;
        if (n == 1)
            return a % p;
        if (n % 2 == 1)
            return a * repeatSquarePow(a, n - 1, p) % p;
        long tmp = repeatSquarePow(a, n / 2, p) % p;
        return tmp * tmp % p;
    }

    public static long modinv(long a, long p) {
        long b, x, u, q, abs_p, tmp;
        abs_p = Math.abs(p);
        b = p;
        x = 1;
        u = 0;
        while (b > 0) {
            q = a / b;
            tmp = u;
            u = x - q * u;
            x = tmp;
            tmp = b;
            b = a - q * b;
            a = tmp;
        }
        return (x < 0) ? abs_p + x : x;
    }

    public static Long[] eratosthenes(int n) {
        Long[] factor_table = new Long[n];
        for (long i = 1; i <= n; i++) {
            factor_table[(int) (i - 1)] = i;
        }
        for (long i = 1; i <= n; i++) {
            if (factor_table[(int) (i - 1)] == i) {
                int j = 2;
                while (i * j <= n) {
                    factor_table[(int) (i * j - 1)] = i;
                    j++;
                }
            }
        }

        return factor_table;
    }

    public static HashMap<Long, Integer> primeFactorization(long n) {
        HashMap<Long, Integer> primes = new HashMap<>();
        for (long p = 2; p * p <= n; p++) {
            int q = 0;
            while (n % p == 0) {
                n /= p;
                q++;
            }
            if (q > 0)
                primes.put(p, q);
        }
        if (n > 1)
            primes.put(n, 1);
        return primes;
    }

    public static ArrayList<Integer> divisor(int n) {
        ArrayList<Integer> ret = new ArrayList<Integer>();
        for (int i = 1; i * i <= n; i++) {
            if (n % i == 0) {
                ret.add(i);
                // n=PQ+0→ PもQも約数. ただし、Q=Pは↑で登録済みなので登録しない
                if (i != n / i)
                    ret.add(n / i);
            }
        }
        return ret;
    }
}

class nextPermutation {
    public static int[] swap(int data[], int left, int right) {

        // Swap the data
        int temp = data[left];
        data[left] = data[right];
        data[right] = temp;

        // Return the updated array
        return data;
    }

    // Function to reverse the sub-array
    // starting from left to the right
    // both inclusive
    public static int[] reverse(int data[], int left, int right) {

        // Reverse the sub-array
        while (left < right) {
            int temp = data[left];
            data[left++] = data[right];
            data[right--] = temp;
        }

        // Return the updated array
        return data;
    }

    // Function to find the next permutation
    // of the given integer array
    public static boolean findNextPermutation(int data[]) {

        // If the given dataset is empty
        // or contains only one element
        // next_permutation is not possible
        if (data.length <= 1)
            return false;

        int last = data.length - 2;

        // find the longest non-increasing suffix
        // and find the pivot
        while (last >= 0) {
            if (data[last] < data[last + 1]) {
                break;
            }
            last--;
        }

        // If there is no increasing pair
        // there is no higher order permutation
        if (last < 0)
            return false;

        int nextGreater = data.length - 1;

        // Find the rightmost successor to the pivot
        for (int i = data.length - 1; i > last; i--) {
            if (data[i] > data[last]) {
                nextGreater = i;
                break;
            }
        }

        // Swap the successor and the pivot
        data = swap(data, nextGreater, last);

        // Reverse the suffix
        data = reverse(data, last + 1, data.length - 1);

        // Return true as the next_permutation is done
        return true;
    }
}

class ArrayUtil {
    private static long INF = 1_000_000_000_0L;

    public static int UpperBound(long[] array, long obj) {
        int l = 0, r = array.length - 1;
        while (r - l >= 0) {
            int c = (l + r) / 2;
            if (obj < array[c]) {
                r = c - 1;
            } else {
                l = c + 1;
            }
        }
        return l;
    }

    public static int LowerBound(long[] array, long obj) {
        int l = 0, r = array.length - 1;
        while (r - l >= 0) {
            int c = (l + r) / 2;
            if (obj <= array[c]) {
                r = c - 1;
            } else {
                l = c + 1;
            }
        }
        return l;
    }

    // return the length of array's LIS
    public static int LIS(long[] array) {
        long[] dp = new long[array.length + 1];
        Arrays.fill(dp, INF);
        for (int i = 0; i < array.length; i++) {
            int idx = LowerBound(dp, array[i]);
            dp[idx] = array[i];
        }
        return LowerBound(dp, INF - 1);
    }

    public static int StrictLIS(long[] array) {
        long[] dp = new long[array.length + 1];
        Arrays.fill(dp, INF);
        for (int i = 0; i < array.length; i++) {
            int idx = UpperBound(dp, array[i]);
            dp[idx] = array[i];
        }
        return UpperBound(dp, INF - 1);
    }
}

class BinaryIndexedTree {
    int[] data;
    long[] tree;
    int n;

    public BinaryIndexedTree(int[] data) {
        this.data = data;
        this.n = data.length;
        this.tree = new long[n + 1];
        buildTree();
    }

    public void buildTree() {
        for (int i = 0; i < n; i++) {
            add(i + 1, data[i]);
        }
    }

    public void add(int index, int value) {
        for (int i = index; i <= n; i += i & -i) {
            tree[i] += value;
        }
    }

    public long sum(int from, int to) {
        return sum(to) - sum(from - 1);
    }

    public long sum(int index) {
        int sum = 0;
        for (int i = index; i > 0; i -= i & -i) {
            sum += tree[i];
        }
        return sum;
    }
}