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 static Assistant.Input;
using static Assistant.Debug;
using System.Linq;
using Assistant;
using System.Text;

namespace 東京海上日動2020D
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = RInt;
            int[] v = new int[n + 1];
            int[] w = new int[n + 1];
            for (int i = 1; i <= n; i++)
            {
                v[i] = RInt;
                w[i] = RInt;
            }

            int L = 100010;

            int half = 12;
            int count = Math.Min(1 << half, n); //2*10^8
            int[,] dp = new int[count + 1, L];
            for (int i = 1; i <= count; i++)
            {
                for (int j = 0; j < L; j++)
                {
                    if (j < w[i]) dp[i, j] = dp[i / 2, j];
                    else dp[i, j] = Math.Max(dp[i / 2, j], dp[i / 2, j - w[i]] + v[i]);
                }
            }

            //Draw2D(dp);

            int Q = RInt;
            StringBuilder sb = new StringBuilder();
            for (int i = 0; i < Q; i++)
            {
                int vq = RInt;
                int lq = RInt;

                List<int> vs = new List<int>();
                while (vq >= (1 << half))
                {
                    vs.Add(vq);
                    vq /= 2;
                }
                int vslast = vq;

                if (vs.Count == 0)
                {
                    sb.AppendLine(dp[vslast, lq].ToString());
                }
                else
                {
                    //bit全探索
                    int c = vs.Count;
                    int ans = 0;
                    for (int bit = 0; bit < (1 << c); ++bit)
                    {
                        int v2 = 0;
                        int w2 = 0;
                        for (int d = 0; d < c; d++)
                        {
                            if ((bit & (1 << d)) != 0)
                            {
                                v2 += v[vs[d]];
                                w2 += w[vs[d]];
                            }
                        }

                        int cand = dp[vslast, Math.Max(0, lq - w2)] + v2;
                        if (w2 > lq) cand = 0;
                        ans = Math.Max(cand, ans);
                    }
                    sb.AppendLine(ans.ToString());
                }
            }
            Console.Write(sb);
        }
    }
}

namespace Assistant
{
    static class Input
    {
        static List<string> line = new List<string>();
        static int index = 0;
        static String RNext()
        {
            if (line.Count <= index) line.AddRange(Console.ReadLine().Split());
            return line[index++];
        }
        public static int RInt => int.Parse(RNext());
        public static long RLong => long.Parse(RNext());
        public static int[] RInts => Console.ReadLine().Split().Select(int.Parse).ToArray();
        public static long[] RLongs => Console.ReadLine().Split().Select(long.Parse).ToArray();
        public static string RString => RNext();
        //以下未テスト
        public static int[] RIntsC(int c) => Enumerable.Repeat(0, c).Select(x => int.Parse(RNext())).ToArray();
        public static long[] RLongsC(int c) => Enumerable.Repeat(0, c).Select(x => long.Parse(RNext())).ToArray();
        public static char[][] RMap(int h) => Enumerable.Repeat(0, h).Select(x => Console.ReadLine().ToCharArray()).ToArray();
    }

    static class Debug
    {
        static public void Draw2D<T>(T[,] map, int mode = 1)
        {
#if DEBUG
            int W = map.GetLength(0);
            int H = map.GetLength(1);

            string[,] map2 = new string[W + 1, H + 1];
            for (int i = 0; i < W + 1; i++)
            {
                for (int j = 0; j < H + 1; j++)
                {
                    if (i == 0 && j == 0) map2[i, j] = 0.ToString();
                    else if (i == 0) map2[i, j] = (j - 1).ToString();
                    else if (j == 0) map2[i, j] = (i - 1).ToString();
                    else map2[i, j] = map[i - 1, j - 1].ToString();
                }
            }

            for (int i = 0; i < W + 1; i++)
            {
                for (int j = 0; j < H + 1; j++)
                {
                    if (mode == 0) Console.Write(map2[i, j].Last());
                    if (mode == 1) Console.Write(map2[i, j] + " ");
                }
                Console.WriteLine();
            }
            Console.WriteLine();
#endif
        }

        public static void Draw1D<T>(T[] array, int mode = 0)
        {
#if DEBUG
            Console.WriteLine(string.Join(" ", array));
#endif
        }
    }
}