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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <utility>
#include <tuple>
#include <vector>
#include <string>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <algorithm>
#include <functional>
#include <climits>
#include <numeric>
#include <queue>
#include <cmath>
#include <iomanip>
#include <array>
#include <string>
#include <stack>
#include <cassert>
#include <memory>

using namespace std;
struct Node {
	int value, weight;
};
int bit_length(const int value) {
	return value == 0 ? 0 : bit_length(value >> 1) + 1;
}
int main() {
	constexpr int l_max = 100000;
	int n; cin >> n;
	vector<Node> nodes(n);
	for (auto& node : nodes) cin >> node.value >> node.weight;
	std::vector<std::vector<std::pair<int, long long int>>> half(1 << (bit_length(n) >> 1));
	half[0].emplace_back(0, 0); if (nodes.front().weight <= l_max) half[0].emplace_back(nodes.front().weight, nodes.front().value);
	for (auto d = 0; d < bit_length(n) >> 1; ++d) {
		const auto len = half.size() >> d;
		for (auto i = 0; i * len < half.size(); ++i) {
			half[i * len + (len >> 1)] = half[i * len];
			for (auto j = 0; j < 2; ++j) {
				if ((2 << d) + i * len + j - 1>= n) continue;
				const auto node = nodes[(2 << d) + i * len + j - 1];
				const auto p = i * len + j * (len >> 1);
				for (int k = half[p].size() - 1; k >= 0; --k) {
					if (node.weight + half[p][k].first > l_max) continue;
					half[p].emplace_back(node.weight + half[p][k].first, node.value + half[p][k].second);
				}
			}
		}
	}
	const auto comparator = [](const std::pair<int, long long int>& a, const std::pair<int, long long int>& b) {return a.first == b.first ? a.second > b.second : a.first < b.first; };
	const auto distinct = [](const std::pair<int, long long int>& a, const std::pair<int, long long int>& b) {return a.first == b.first; };
	for (auto& s : half) {
		std::sort(s.begin(), s.end(), comparator);
		for (auto i = 1; i < s.size(); ++i) {
			s[i].second = std::max(s[i].second, s[i - 1].second);
		}
		s.erase(std::unique(s.begin(), s.end(), distinct), s.end());
	}
	int q; std::cin >> q;
	const auto cached = 1 << (bit_length(n) >> 1);
	const auto finder = [](const int value, const std::pair<int, long long int>& a) {return a.first > value; };
	for (; q > 0; --q) {
		int u, l; std::cin >> u >> l;
		if (u >= cached) {
			std::vector<std::pair<int, long long int>> until_cached{std::make_pair(0, 0)};
			while (u >= (cached << 1)) {
				const auto node = nodes[u - 1];
				for (int i = until_cached.size() - 1; i >= 0; --i) {
					if (node.weight + until_cached[i].first > l) continue;
					until_cached.emplace_back(node.weight + until_cached[i].first, node.value + until_cached[i].second);
				}
				u >>= 1;
			}
			long long int result{ 0 };
			for (const auto& pair : until_cached) {
				const auto pos = std::distance(half[u - cached].begin(), std::upper_bound(half[u - cached].begin(), half[u - cached].end(), l - pair.first, finder));
				if (pos > 0) {
					result = std::max(result, half[u - cached][pos - 1].second + pair.second);
				}
			}
			std::cout << result << '\n';
		}
		else {
			std::vector<std::pair<int, long long int>> until_cached{ std::make_pair(0, 0) };
			while (u > 0) {
				const auto node = nodes[u - 1];
				for (int i = until_cached.size() - 1; i >= 0; --i) {
					if (node.weight + until_cached[i].first > l) continue;
					until_cached.emplace_back(node.weight + until_cached[i].first, node.value + until_cached[i].second);
				}
				u >>= 1;
			}
			long long int result{ 0 };
			for (const auto& pair : until_cached) {
				result = std::max(result, pair.second);
			}
			std::cout << result << '\n';
		}
	}
}