Problem:
Score : 700 points

Problem Statement

We have a rooted binary tree with N vertices, where the vertices are numbered 1 to N.
Vertex 1 is the root, and the parent of Vertex i (i \geq 2) is Vertex \left[ \frac{i}{2} \right].

Each vertex has one item in it. The item in Vertex i has a value of V_i and a weight of W_i.
Now, process the following query Q times:

Given are a vertex v of the tree and a positive integer L.
Let us choose some (possibly none) of the items in v and the ancestors of v so that their total weight is at most L.
Find the maximum possible total value of the chosen items.

Here, Vertex u is said to be an ancestor of Vertex v when u is an indirect parent of v, that is, there exists a sequence of vertices w_1,w_2,\ldots,w_k (k\geq 2) where w_1=v, w_k=u, and w_{i+1} is the parent of w_i for each i.

Constraints

All values in input are integers.

1 \leq N < 2^{18}

1 \leq Q \leq 10^5

1 \leq V_i \leq 10^5

1 \leq W_i \leq 10^5

For the values v and L given in each query, 1 \leq v \leq N and 1 \leq L \leq 10^5.

Input

Let v_i and L_i be the values v and L given in the i-th query.
Then, Input is given from Standard Input in the following format:

N
V_1 W_1
:
V_N W_N
Q
v_1 L_1
:
v_Q L_Q

Output

For each integer i from 1 through Q,
the i-th line should contain the response to the i-th query.

Sample Input 1

3
1 2
2 3
3 4
3
1 1
2 5
3 5

Sample Output 1

0
3
3

In the first query, we are given only one choice: the item with (V, W)=(1,2). Since L = 1, we cannot actually choose it, so our response should be 0.

In the second query, we are given two choices: the items with (V, W)=(1,2) and (V, W)=(2,3). Since L = 5, we can choose both of them, so our response should be 3.

Sample Input 2

15
123 119
129 120
132 112
126 109
118 103
115 109
102 100
130 120
105 105
132 115
104 102
107 107
127 116
121 104
121 115
8
8 234
9 244
10 226
11 227
12 240
13 237
14 206
15 227

Sample Output 2

256
255
250
247
255
259
223
253

Solution in Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)


import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;

import java.util.*;

public class Main {
    long MOD = (long) 1e9 + 7;

    InputStream in;
    OutputStream out;

    public Main() {
        this(System.in, System.out);
    }

    public Main(InputStream in, OutputStream out) {
        this.in = in;
        this.out = out;
    }
    int n;
    int[] V, W;

    void run() {
        Scanner sc = new Scanner(this.in);
        PrintWriter out = new PrintWriter(this.out);

        // write your code
        n = sc.nextInt();
        V = new int[n];
        W = new int[n];
        for (int i = 0; i < n; i++) {
            V[i] = sc.nextInt();
            W[i] = sc.nextInt();
        }

        int q = sc.nextInt();
        for (int i = 0; i < q; i++) {
            int v = sc.nextInt(), l = sc.nextInt();
            ArrayList<Integer> nodes = new ArrayList<>();
            while (v > 0) {
                nodes.add(v - 1);
                v /= 2;
            }
            out.println(solve(nodes, l));
        }


        out.flush();
    }

    long solve(ArrayList<Integer> nodes, int l) {

        int size = nodes.size();

        ArrayList<Integer> left = new ArrayList<>(), right = new ArrayList<>();
        for (int i = 0; i < size; i++) {
            if (i < size / 2) {
                left.add(nodes.get(i));
            } else {
                right.add(nodes.get(i));
            }
        }

        ArrayList<Pair> lp = enumerate(left, size / 2);
        ArrayList<Pair> rp = enumerate(right, size - size / 2);
        int rsize = rp.size();

        long max = 0;
        for (Pair p : lp) {
            if (l - p.ws < 0) continue;
            int idx = upperBound(rp, l - p.ws);
            if (idx == rsize) idx--;
//            debug(p, l, idx, rp.get(idx));
            max = Math.max(max, p.vs + rp.get(idx).vs);
        }

        return max;
    }

    ArrayList<Pair> enumerate(ArrayList<Integer> nodes, int size) {
        HashMap<Long, Long> map = new HashMap<>();
        for (int i = 0; i < (1 << size); i++) {
            long ws = 0, vs = 0;
            for (int j = 0; j < size; j++) {
                if (((i >> j) & 1) == 1) {
                    ws += W[nodes.get(j)];
                    vs += V[nodes.get(j)];
                }
            }
            long cv = map.getOrDefault(ws, 0L);
            map.put(ws, Math.max(cv, vs));
        }

        ArrayList<Pair> ret = new ArrayList<>();
        for (Map.Entry<Long, Long> entry : map.entrySet()) {
            ret.add(new Pair(entry.getValue(), entry.getKey()));
        }
        Collections.sort(ret);
        int s = ret.size();
        for (int i = 1; i < s; i++) {
            if (ret.get(i - 1).vs > ret.get(i).vs) {
                ret.get(i).vs = ret.get(i - 1).vs;
            }
        }
        return ret;
    }

    public int upperBound(ArrayList<Pair> array, long value) {
        int left = -1;
        int right = array.size();
        while (right - left > 1) {
            int middle = (right + left) / 2;
            if (array.get(middle).ws > value) {
                right = middle;
            } else {
                left = middle;
            }
        }
        return left;
    }

    class Pair implements Comparable<Pair> {
        long vs, ws;
        Pair(long vs, long ws) {
            this.vs = vs;
            this.ws = ws;
        }

        @Override
        public int compareTo(Pair o) {
            return Long.compare(ws, o.ws);
        }

        @Override
        public String toString() {
            return "(" + vs +", " + ws + ")";
        }
    }

    void debug(Object... os) {
        System.err.println(Arrays.deepToString(os));
    }

    public static void main(String[] args) {
        new Main().run();
    }
}