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;
using System.Text;
using static System.Console;
using static System.Math;

namespace AtTest.TokioMarine_2020
{
    class D
    {
        static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(OpenStandardOutput()) { AutoFlush = false };
            SetOut(sw);

            Method(args);

            Out.Flush();
        }

        static void Method(string[] args)
        {
            int n = ReadInt();
            long[][] vws = new long[n][];
            for(int i = 0; i < n; i++)
            {
                vws[i] = ReadLongs();
            }
            int half = Min(n, 1 << 8 - 1);
            long[,] dp = new long[half, 100000 + 100];
            dp[0, vws[0][1]] = vws[0][0];
            for(int i = 1; i < 100000 + 100; i++)
            {
                dp[0, i] = Max(dp[0, i], dp[0, i - 1]);
            }
            for(int i = 1; i < half; i++)
            {
                for (int j = 0; j < 100000 + 100; j++)
                {
                    dp[i, j] = dp[(i - 1) / 2, j];
                    if (j >= vws[i][1])
                    {
                        dp[i, j] = Max(dp[i, j], dp[(i-1) / 2, j - vws[i][1]] + vws[i][0]);
                    }
                }
                for(int j = 1; j < 100000 + 100; j++)
                {
                    dp[i, j] = Max(dp[i, j], dp[i, j - 1]);
                }
            }

            int q = ReadInt();
            for(int i = 0; i < q; i++)
            {
                int[] vl = ReadInts();
                int v = vl[0] - 1;
                int l = vl[1];

                if (v < half)
                {
                    WriteLine(dp[v, l]);
                }
                else
                {
                    var dict = new Dictionary<int, long>();
                    dict.Add(0, 0);
                    int tmp = v;
                    while (half <= tmp)
                    {
                        var next = new Dictionary<int, long>();
                        foreach(int key in dict.Keys)
                        {
                            if (next.ContainsKey(key))
                            {
                                next[key] = Max(next[key], dict[key]);
                            }
                            else
                            {
                                next.Add(key, dict[key]);
                            }

                            int nextW = key + (int)vws[tmp][1];
                            if (nextW <= l)
                            {
                                if (next.ContainsKey(nextW))
                                {
                                    next[nextW] = Max(next[nextW], dict[key] + vws[tmp][0]);
                                }
                                else
                                {
                                    next.Add(nextW, dict[key] + vws[tmp][0]);
                                }
                            }
                        }
                        dict = next;
                        tmp = (tmp - 1) / 2;
                    }
                    long ans = 0;
                    foreach(int key in dict.Keys)
                    {
                        ans = Max(ans, dict[key] + dp[tmp, l - key]);
                    }
                    WriteLine(ans);
                }
            }
        }

        private static string Read() { return ReadLine(); }
        private static char[] ReadChars() { return Array.ConvertAll(Read().Split(), a => a[0]); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}