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 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Objects;

public class Main {
    private static final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    public static void main(String args[]) throws Exception {
        int n = Integer.parseInt(br.readLine());
        int[] v = new int[n+1];
        int[] w = new int[n+1];
        String[] tokens = null;
        for(int i=1;i<=n;i++){
            tokens = br.readLine().split(" ");
            v[i] = Integer.parseInt(tokens[0]);
            w[i] = Integer.parseInt(tokens[1]);
        }
        int q = Integer.parseInt(br.readLine());;
        while(q-->0){
            tokens = br.readLine().split(" ");
            int vertex = Integer.parseInt(tokens[0]);
            int l  = Integer.parseInt(tokens[1]);
            System.out.println(solve(v,w,vertex,l));
        }
    }

    private static long solve(int[] v,int w[],int vertex,int l){
        List<Integer> vals = new ArrayList<>();
        List<Integer> wts = new ArrayList<>();
        int vert = vertex;
        while(vert>=1){
            vals.add(v[vert]);
            wts.add(w[vert]);
            vert>>=1;
        }
        long[][] dp = new long[vals.size()][l+1];
        init(dp);
        return knapsack(vals,wts,vals.size()-1,l,dp);
    }

    private static void init(long[][] dp){
        for(int i=0;i<dp.length;i++){
            Arrays.fill(dp[i],-1);
        }
    }

    private static long knapsack(List<Integer> vals,List<Integer> wts,int vertex,int l,long[][] dp){
        if(vertex<0)
            return 0;
        if(dp[vertex][l]!=-1)
            return dp[vertex][l];
        long ans = knapsack(vals,wts,vertex-1,l,dp);
        if(wts.get(vertex)<=l)
            ans = Math.max(ans,knapsack(vals,wts,vertex-1,l-wts.get(vertex),dp)+vals.get(vertex));
        dp[vertex][l] = ans;
        return ans;
    }



}