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 C# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;

namespace ProblemD
{
    class Program
    {
        static void Main()
        {
            long N = GetLong();
            var items = new long[N][];
            for(int i = 0; i < N; i++)
            {
                items[i] = GetLongArray();
            }
            long Q = GetLong();
            var query = new long[Q][];
            for(int i = 0; i < Q; i++)
            {
                query[i] = GetLongArray();
            }

            for(int i = 0; i < Q; i++)
            {
                var list = new List<long> { query[i][0]};
                var temp = query[i][0];
                while(temp != 1)
                {
                    temp /= 2;
                    list.Add(temp);
                }
                
                var dp = new long[list.Count][];
                for(int j = 0; j < list.Count; j++)
                {
                    dp[j] = new long[query[i][1] + 1];
                    for(int k = 0; k <= query[i][1]; k++)
                    {
                        if (j == 0)
                        {
                            dp[j][k] = k >= items[list[j] - 1][1] ? items[list[j] - 1][0] : 0;
                        }
                        else if (k == 0)
                        {
                            dp[j][k] = 0;
                        }
                        else if(k - items[list[j] - 1][1] < 0)
                        {
                            dp[j][k] = dp[j - 1][k];
                        }
                        else
                        {
                            dp[j][k] = Math.Max(dp[j - 1][k], dp[j - 1][k - items[list[j] - 1][1]] + items[list[j] - 1][0]);
                        }
                    }
                }
                Console.WriteLine(dp[list.Count - 1][query[i][1]]);
            }
        }

        //入力関係のメソッド
        public static int GetInt() => int.Parse(Console.ReadLine());
        public static int[] GetIntArray() => Console.ReadLine().Split().Select(int.Parse).ToArray();
        public static double GetDouble() => double.Parse(Console.ReadLine());
        public static double[] GetDoubleArray() => Console.ReadLine().Split().Select(double.Parse).ToArray();
        public static long GetLong() => long.Parse(Console.ReadLine());
        public static long[] GetLongArray() => Console.ReadLine().Split().Select(long.Parse).ToArray();

        //出力関係のメソッド
        public static void OutIntArray(int[] values)
        {
            foreach (var value in values)
            {
                Console.WriteLine(value);
            }
        }
        public static void OutLongArray(long[] values)
        {
            foreach (var value in values)
            {
                Console.WriteLine(value);
            }
        }
        public static void OutList(List<object> list)
        {
            foreach (var value in list)
            {
                Console.WriteLine(value);
            }
        }

    }
}