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: Runtime Error)

#include "bits/stdc++.h"
#include "ext/pb_ds/assoc_container.hpp"
#include "ext/pb_ds/tree_policy.hpp"
#include "ext/rope"
using namespace std;
using namespace chrono;
using namespace __gnu_pbds;
using namespace __gnu_cxx;
mt19937 rng(high_resolution_clock::now().time_since_epoch().count());
mt19937_64 rngll(high_resolution_clock::now().time_since_epoch().count());
#define lambdify(x) [&](auto &&...args){ return x(forward<decltype(args)>(args)...); }
template<typename T, typename U> T &ctmax(T &x, const U &y){ return x = max<T>(x, y); }
template<typename T, typename U> T &ctmin(T &x, const U &y){ return x = min<T>(x, y); }
template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;



int main(){
	cin.tie(0)->sync_with_stdio(0);
	int n;
	cin >> n;
	const int mx = 1e5;
	vector<array<int, 2>> val(n); // value, weight
	for(auto i = 0; i < n; ++ i){
		for(auto j = 0; j < 2; ++ j){
			cin >> val[i][j];
		}
	}
	const int h = 9;
	vector<vector<long long>> dp((1 << h) - 1, vector<long long>(mx + 1));
	// dp[u][x]: max value obtainable for node u with weight at most x
	for(auto x = val[0][1]; x <= mx; ++ x){
		dp[0][x] = val[0][0];
	}
	for(auto u = 1; u < min((1 << h) - 1, n); ++ u){
		int p = u - 1 >> 1;
		dp[u] = dp[p];
		for(auto x = mx; x >= val[u][1]; -- x){
			ctmax(dp[u][x], max(dp[p][x - val[u][1]] + val[u][0], dp[u][x - 1]));
		}
	}
	int qq;
	cin >> qq;
	while(qq --){
		int u, x;
		cin >> u >> x, -- u;
		int ch = __lg(u + 1);
		if(ch < h){
			cout << dp[u][x] << "\n";
		}
		else{
			int d = ch - h + 1, p = u >> d;
			long long res = 0;
			for(auto mask = 0; mask < 1 << d; ++ mask){
				long long cv = 0, cw = 0;
				for(auto bit = 0; bit < d; ++ bit){
					if(mask & 1 << bit){
						cv += val[u >> bit][0];
						cw += val[u >> bit][1];
					}
				}
				if(cw <= x){
					ctmax(res, dp[p][x - cw] + cv);
				}
			}
			cout << res << "\n";
		}
	}
	return 0;
}

/*

*/

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//                                                                                    //
//                                   Coded by Aeren                                   //
//                                                                                    //
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