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: Accepted)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;
#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
#[allow(unused_imports)]
use std::f64::consts::*;
use superslice::*;

#[allow(unused)]
const INF: usize = std::usize::MAX / 4;
#[allow(unused)]
const M: usize = 1000000007;

fn main() {
    input! {
        n: usize,
        vw: [(usize, usize); n],
        q: usize,
        ul: [(Usize1, usize); q],
    }
    let w_max = 100000;
    let mut states = vec![vec![]; n];
    states[0].push((0, 0));
    states[0].push(vw[0]);
    for i in 1..min(n, 2usize.pow(10)) {
        let (vi, wi) = vw[i];
        let p = (i + 1) / 2 - 1;
        let mut candidates = vec![];
        for &(vp, wp) in &states[p] {
            candidates.push((vp, wp));
            if wi + wp <= w_max {
                candidates.push((vi + vp, wi + wp));
            }
        }
        candidates.sort_by_key(|&(vs, ws)| (ws, Reverse(vs)));
        // eprintln!("{:?}", candidates);
        states[i].push(candidates[0]);
        for j in 1..candidates.len() {
            let (vj, wj) = candidates[j];
            let (vq, _) = states[i][states[i].len() - 1];
            if vj > vq {
                states[i].push((vj, wj));
            }
        }
    }
    for &(u, l) in &ul {
        let result = if states[u].is_empty() {
            let mut vw_local = vec![];
            let mut p = u;
            while states[p].is_empty() {
                vw_local.push(vw[p]);
                p = (p + 1) / 2 - 1;
            }
            // eprintln!("{} {:?}", u, vw_local);
            let m = vw_local.len();
            let mut result = 0;
            for x in 0..2usize.pow(m as u32) {
                let mut s_v = 0;
                let mut s_w = 0;
                for i in 0..m {
                    if x & 1 << i > 0 {
                        s_v += vw_local[i].0;
                        s_w += vw_local[i].1;
                    }
                }
                if s_w <= l {
                    let k = states[p].upper_bound_by_key(&(l - s_w), |&(_, wk)| wk) - 1;
                    result = max(result, states[p][k].0 + s_v);
                }
            }
            result
        } else {
            let k = states[u].upper_bound_by_key(&l, |&(_, wk)| wk) - 1;
            states[u][k].0
        };
        println!("{}", result);
    }
}
*/

fn main() {
    let exe = "/tmp/bin12C1C8B3";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";