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# (Mono-mcs 6.8.0.105) (judge verdict: Wrong Answer)

using System;
using System.Collections;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using System.Collections.Generic;
using System.Threading.Tasks;

class Program
{
	//頂点数
	static int N;
	//価値と重さを格納する配列
	static int[,] nodeData;

	//毎回DP
	static int DP(int start, int limit){
		//DP配列（頂点, 重さ制限）：毎回上書き
		int[,] dp = new int[2,limit+1];

		int current = start;
		int cnt = 0;

		//初期化
		for(int i=0; i<limit+1; i++){
			if(nodeData[current,1] <= i){
				dp[0,i] = nodeData[current,0];
			}
		}

		current /= 2;
		int child = 0;
		int parent = 1;

		//下から埋める
		while(current > 0){
			if(cnt % 2 == 0){
				child = 0;
				parent = 1;
			}else{
				child = 1;
				parent = 0;
			}
			for(int j=0; j<limit+1; j++){
				//自分自身の価値と重さ
				int val = nodeData[current,0];
				int wei = nodeData[current,1];

				//自分自身を選ぶ場合
				int choose = 0;
				if(wei <= j){
					choose = dp[child,j-wei] + val;
				}

				//自分自身を選ばない場合と比べ、大きい方
				int res = Math.Max(dp[child,j], choose);
				dp[parent,j] = res;
			}

			current /= 2;
			cnt ++;
		}

		return dp[parent,limit];

	}

	//Main
	static void Main(string[] args)
	{
		//読み込む
		N = int.Parse(Console.ReadLine());

		//初期化と読み込み
		nodeData = new int[N+1,2];
		for(int i=0; i<N; i++){
			string[] line = Console.ReadLine().Split(' ');
			//価値
			nodeData[i+1,0] = int.Parse(line[0]);
			//重さ
			nodeData[i+1,1] = int.Parse(line[1]);
		}

		//クエリに答える
		int Q = int.Parse(Console.ReadLine());

		//カード読み込む
		for(int i=0; i<Q; i++){
			string[] line = Console.ReadLine().Split(' ');
			//頂点
			int v = int.Parse(line[0]);
			//制限
			int L = int.Parse(line[1]);

			//出力
			Console.WriteLine(DP(v,L));
		}
	}
}