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 Rust (1.42.0) (judge verdict: Wrong Answer)

#[allow(unused_imports)]
use proconio::{input, marker::*};

#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};

#[allow(unused_imports)]
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        #[cfg(debug_assertions)]
        writeln!(&mut std::io::stderr(), concat!("[DEBUG] ", $(stringify!($a), "={:?} "),*), $($a),*).unwrap();
    }
}

fn lower_bound<F>(l: usize, r: usize, criterion: F) -> usize
where
    F: Fn(usize) -> bool,
{
    let mut l = l;
    let mut r = r;
    while r - l > 1 {
        let mid = l + (r - l) / 2;
        if criterion(mid) {
            r = mid;
        } else {
            l = mid;
        }
    }
    r
}

macro_rules ! max { ( $ x : expr ) => ( $ x ) ; ( $ x : expr , $ ( $ z : expr ) ,+ ) => { { std :: cmp :: max ( $ x , max ! ( $ ( $ z ) ,* ) ) } } }

fn main() {
    input! {
        n: usize,
        vw: [(usize, usize);n],
        q: usize,
        vl: [(Usize1, usize);q],
    }

    for &(v, l) in &vl {
        let mut vec = Vec::new();
        let mut i = v;
        vec.push(i);
        while i > 0 {
            i = (i - 1) / 2;
            vec.push(i);
        }

        let half = vec.len() / 2;
        let full = vec.len();
        let mut left = vec![(0, 0); 1 << half];
        for i in 0..1 << half {
            let mut weight = 0;
            let mut val = 0;
            for j in 0..half {
                let (v, w) = vw[vec[j]];
                if (i >> j) & 1 == 0 {
                    continue;
                }
                weight += w;
                val += v;
            }
            left[i] = (weight, val);
        }
        left.sort();

        let mut mx = 0;
        for i in 0..1 << (full - half) {
            let mut weight = 0;
            let mut val = 0;
            for j in 0..(full - half) {
                let (v, w) = vw[vec[j + half]];
                if (i >> j) & 1 == 0 {
                    continue;
                }
                weight += w;
                val += v;
            }
            if weight > l {
                continue;
            }
            let crit = |i: usize| left[i].0 + weight > l;
            let i = lower_bound(0, 1 << half, crit) - 1;
            mx = max!(mx, left[i].1 + val);
        }
        println!("{}", mx);
    }
}