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: Accepted)

using System;
using System.Collections.Generic;
using System.Collections;
using System.Collections.Specialized;
using System.Linq;
using System.Text;
using System.IO;
using System.Reflection;
using static System.Math;
using System.Numerics;
using System.Runtime.CompilerServices;
static class Program{
	const int mod=(int)1e9+7;
	const double eps=1e-11;
	static void Main(){
		Sc sc=new Sc();
		var n=sc.I;
		var h=new int[n+1][];
		var ma=new int[n+1];
		int d=12,m=Min((1<<d)-1,n);
		int g=(int)Log(m,2);
		var dp=new (int v,int w)[n+1][];
		h[0]=new int[2];
		dp[0]=new (int,int)[1];
		dp[0][0]=(0,0);
		ma[0]=1;
		var z=new (int v,int w)[1<<d+1];
		for(int i = 1;i<=n;i++) {
			h[i]=sc.Ia;
			if(i<=m){Fu(i,i>>1);}
		}
		var q=sc.I;
		var ans=new int[q];
		for(int i = 0;i<q;i++) {
			var e=sc.Ia;
			if(e[0]<=m){
				int lb=0,ub=ma[e[0]],mid=0;
				while(lb+1!=ub){
					mid=(ub+lb)>>1;
					if(dp[e[0]][mid].w>e[1]){ub=mid;}
					else{lb=mid;}
				}
				ans[i]=dp[e[0]][lb].v;
			}
			else{
				int p=((int)Log(e[0],2))-g-1,r=0,u=e[0]>>(p+1);
				if(ma[e[0]]==0){
					while(p>=0){
						if(ma[e[0]>>p]==0){Fu(e[0]>>p,r);}
						r=e[0]>>p;
						p--;
					}
				}
				for(int j = 0,k=ma[e[0]]-1;j<ma[u];j++) {
					while(k!=0&&dp[u][j].w+dp[e[0]][k].w>e[1]){k--;}
					if(dp[u][j].w+dp[e[0]][k].w<=e[1]){ans[i]=Max(ans[i],dp[u][j].v+dp[e[0]][k].v);}
				}
			}
		}
		Console.WriteLine("{0}",String.Join("\n",ans));
		void Fu(int i,int p) {
			int o=ma[p]<<1;
			dp[i]=new (int,int)[o];
			int k=0,l=0;
			for(int j = 0;j<dp[p].Length;j++) {
				z[j]=(dp[p][j].v+h[i][0],dp[p][j].w+h[i][1]);
				while(l<=j&&dp[p][j].w>z[l].w){
					if(k==0||dp[i][k-1].v<z[l].v){
						if(k!=0&&dp[i][k-1].w==z[l].w){dp[i][k-1].v=z[l].v;}
						else{
							dp[i][k]=z[l];
							k++;
						}
					}
					l++;
				}
				if(k==0||dp[i][k-1].v<dp[p][j].v){
					if(k!=0&&dp[i][k-1].w==dp[p][j].w){dp[i][k-1].v=dp[p][j].v;}
					else{
						dp[i][k]=dp[p][j];
						k++;
					}
				}
			}
			for(;l<ma[p];l++) {
				if(dp[i][k-1].v<z[l].v){
					if(dp[i][k-1].w==z[l].w){dp[i][k-1].v=Max(dp[i][k-1].v,z[l].v);}
					else{
						dp[i][k]=z[l];
						k++;
					}
				}
			}
			ma[i]=k;
		}
	}
}
public class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
	public object[] Oa{get{return Console.ReadLine().Split();}}
	public int[] Ia2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),int.Parse);}}
	public int[] Ia3(string a,string b){return Array.ConvertAll((a+Console.ReadLine()+b).Split(),int.Parse);}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),long.Parse);}}
	public long[] La3(string a,string b){return Array.ConvertAll((a+Console.ReadLine()+b).Split(),long.Parse);}
	public double[] Da2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),double.Parse);}}
	public double[] Da3(string a,string b){return Array.ConvertAll((a+Console.ReadLine()+b).Split(),double.Parse);}
	public T[] Arr<T>(int n,Func<T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f();}return a;}
	public T[] Arr<T>(int n,Func<int,T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i);}return a;}
	public T[] Arr<T>(int n,Func<string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(Console.ReadLine().Split());}return a;}
	public T[] Arr<T>(int n,Func<int,string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i,Console.ReadLine().Split());}return a;}
}