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.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.Globalization;
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][];
		for(int i = 1;i<=n;i++) {
			h[i]=sc.Ia;
		}
		var q=sc.I;
		var ans=new int[q];
		for(int i = 0;i<q;i++) {
			var e=sc.Ia;
			int p=e[0],m1=Bsr(p)+1,m2=m1/2;
			m1-=m2;
			var d1=new int[m1][];
			var d2=new int[m2][];
			for(int j = 0;p!=0;j++) {
				if(j<m1){d1[j]=h[p];}
				else{d2[j-m1]=h[p];}
				p>>=1;
			}
			if(m2==0){
				if(e[1]>=d1[0][1]){ans[i]=d1[0][0];}
				continue;
			}
			int g=1<<m1;
			var dp1=new int[g][];
			dp1[0]=new int[]{0,0};
			for(int j = 1,l=1,o=0;j<g;j++) {
				if((l<<1)==j){l=j;o++;}
				dp1[j]=new int[]{dp1[j-l][0]+d1[o][0],dp1[j-l][1]+d1[o][1]};
			}
			g=1<<m2;
			var dp2=new int[g][];
			dp2[0]=new int[]{0,0};
			for(int j = 1,l=1,o=0;j<g;j++) {
				if((l<<1)==j){l=j;o++;}
				dp2[j]=new int[]{dp2[j-l][0]+d2[o][0],dp2[j-l][1]+d2[o][1]};
			}
			Array.Sort(dp1,(u,v)=>u[1]-v[1]);
			Array.Sort(dp2,(u,v)=>u[1]-v[1]);
			var va=new int[1<<m1];
			for(int j = 1;j<1<<m1;j++) {
				va[j]=Max(va[j-1],dp1[j][0]);
			}
			for(int j = 0,k=(1<<m1)-1;j<g;j++) {
				while(k!=0&&dp2[j][1]+dp1[k][1]>e[1]){
					k--;
				}
				if(dp2[j][1]+dp1[k][1]<=e[1]){
					ans[i]=Max(ans[i],dp2[j][0]+va[k]);
				}
			}
		}
		Console.WriteLine("{0}",String.Join("\n",ans));
	}
	static int Bsr(long b){
		int n=0;
		if(b==0){return -1;}
		if((b&-281470681808896)!=0){b=b&-281470681808896;n+=16;}
		if((b&-71777214294589696)!=0){b=b&-71777214294589696;n+=8;}
		if((b&-1085102592571150096)!=0){b=b&-1085102592571150096;n+=4;}
		if((b&-3689348814741910324)!=0){b=b&-3689348814741910324;n+=2;}
		if((b&-6148914691236517206)!=0){b=b&-6148914691236517206;n+=1;}
		return n;
	}
}
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;}
}