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: Wrong Answer)


import java.io.*;
import java.util.Arrays;
import java.util.Scanner;
import java.util.StringTokenizer;

public class Main
{
    public static void print(String str,int val){
        System.out.println(str+"  "+val);
    }



    public static void debug(long[][] arr){
        int len = arr.length;
        for(int i=0;i<len;i++){
            System.out.println(Arrays.toString(arr[i]));
        }
    }
    public static void debug(int[][] arr){
        int len = arr.length;
        for(int i=0;i<len;i++){
            System.out.println(Arrays.toString(arr[i]));
        }
    }
    public static void debug(String[] arr){
        int len = arr.length;
        for(int i=0;i<len;i++){
            System.out.println(arr[i]);
        }
    }

    public static void print(int[] arr){
        int len = arr.length;
        for(int i=0;i<len;i++){
            System.out.print(arr[i]+" ");
        }
        System.out.print('\n');
    }
    public static void print(String[] arr){
        int len = arr.length;
        for(int i=0;i<len;i++){
            System.out.print(arr[i]+" ");
        }
        System.out.print('\n');
    }
    public static void print(long[] arr){
        int len = arr.length;
        for(int i=0;i<len;i++){
            System.out.print(arr[i]+" ");
        }
        System.out.print('\n');
    }

    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

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

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }

    static int[] value;
    static int[] weight;
    static int[][] knapsack;
    static int n;
    public static void compute(){
        for(int i=0;i<=Math.min((1<<9),n);i++){
            for(int w=0;w<=100000;w++){
                if(i==0||w==0){
                    knapsack[i][w] =0;
                }
                else if(weight[i]<=w){
                    knapsack[i][w] = Math.max(knapsack[((i)>>1)][w-weight[i]]+value[i],knapsack[(i)>>1][w]);
                }
                else {
                    knapsack[i][w] = knapsack[((i)>>1)][w];
                }
            }
        }
    }
    public static void main(String[] args)
    {
        FastReader s=new FastReader();
        n = s.nextInt();
        value = new int[n+1];
        weight = new int[n+1];
        knapsack = new int[(1<<9)+1][100000+1];
        for(int i=1;i<=n;i++){
            value[i] = s.nextInt();
            weight[i] = s.nextInt();
        }
        compute();
        int q = s.nextInt();
        while ((q--)>0){
            int vertex = s.nextInt();
            int given_weight = s.nextInt();
            if(vertex<(1<<9)){
                System.out.println(knapsack[vertex][given_weight]);
            }
            else {
//                int max_value = Integer.MIN_VALUE;
//                int log_value = (int)Math.floor(Math.log(vertex)/Math.log(2));
//                int n_bits = log_value-8;
//                for(int mask =0;mask<(1<<n_bits);mask++){
//                    int tot_value =0;
//                    int rem_weight = given_weight;
//                    for(int i=0;i<n_bits;i++){
//                        if((mask&(1<<i))==1){
//                            if(rem_weight>=weight[(vertex/(1<<i))]){
//                                tot_value+=value[((vertex/(1<<i)))];
//                                rem_weight = rem_weight-weight[(vertex/(1<<i))];
//                            }
//                        }
//                    }
//                    if(rem_weight>0){
//                        tot_value+=knapsack[(vertex/(1<<n_bits))][rem_weight];
//                    }
//                    max_value = Math.max(max_value,tot_value);
//                }
                int max_value = knap(vertex,given_weight);
                System.out.println(max_value);
            }
        }

    }
    public static int knap(int vertex,int w){
        if(w<=0){
            return 0;
        }

        if(vertex<(1<<9)){
            return knapsack[vertex][w];
        }
        if(weight[vertex]<=w){
            return Math.max(knap((vertex>>1),w-weight[vertex]),knap((vertex>>1),w));
        }
        return knap((vertex>>1),w);
    }




//    OutputStream out = new BufferedOutputStream( System.out );
//        for(int i=1;i<n;i++){
//    out.write((arr[i]+" ").getBytes());
//}
//        out.flush();

    //  long start = System.currentTimeMillis();
//  long end = System.currentTimeMillis();
//  System.out.println((end - start) + "ms");



}