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: Time Limit Exceeded)

#![allow(non_snake_case)]

#[allow(unused_macros)]
macro_rules! debug {
    ( $x:ident [ $i:expr ] ) => {
        if cfg!(debug_assertions) {
            println!("{}[{}] = {:?}", stringify!($x), $i, $x[$i]);
        }
    };
    ( $x:ident [ $i:expr ][ $j:expr ] ) => {
        if cfg!(debug_assertions) {
            println!("{}[{}][{}] = {:?}", stringify!($x), $i, $j, $x[$i][$j]);
        }
    };
    ( $x:expr ) => {
        if cfg!(debug_assertions) {
            println!("{}:{} {} = {:?}", line!(), column!(), stringify!($x), $x);
        }
    };
}

fn _knapsack_dp(items: &[(u64, u64)], capacity: u64) -> Vec<(u64, u64)> {
    let n = items.len();
    (0..(1 << n)).map(|b| {
            (0..n).filter(|&i| b & (1 << i) != 0)
                .map(|i| items[i])
                .fold((0, 0), |(acc_weight, acc_value), (weight, value)| (acc_weight + weight, acc_value + value))
        }).filter(|&(sum_weight, _sum_value)| sum_weight <= capacity)
        .collect()
}

pub fn knapsack(items: &[(u64, u64)], capacity: u64) -> u64 {
    let n = items.len();
    let a1 = _knapsack_dp(&items[..n / 2], capacity);
    let mut a2 = _knapsack_dp(&items[n / 2..], capacity);
    a2.sort();

    let mut acc_max_value = vec![0; a2.len() + 1];
    for i in 0..a2.len() {
        acc_max_value[i + 1] = std::cmp::max(acc_max_value[i], a2[i].1);
    }

    let mut result = 0;
    for (weight1, value1) in a1 {
        let value2 = acc_max_value[upper_bound(&a2, (capacity - weight1, std::u64::MAX))];
        result = std::cmp::max(result, value1 + value2);
    }
    result
}

fn upper_bound<T: Ord>(a: &[T], x: T) -> usize {
    let mut first = 0;
    let mut last = a.len();
    loop {
        let n = last - first;
        if n == 0 { break; }
        let mid = first + n / 2;
        if a[mid] <= x {
            first = mid + 1;
        } else {
            last = mid;
        }
    }
    first
}

fn main() {
    use std::io::Write;

    let stdin = std::io::stdin();
    let mut stdin = my::io::InputReader::new(stdin.lock());
    let stdout = std::io::stdout();
    let mut out = std::io::BufWriter::new(stdout.lock());

    let N: usize = stdin.read();
    let mut items = vec![(0u64, 0u64); N + 1];
    for i in 1..=N {
        let V: u64 = stdin.read();
        let W: u64 = stdin.read();
        items[i] = (W, V);
    }
    let Q: usize = stdin.read();
    for _ in 0..Q {
        let mut v: usize = stdin.read();
        let L: u64 = stdin.read();
        let mut path_items = Vec::<(u64, u64)>::new();
        while v > 0 {
            path_items.push(items[v]);
            v /= 2;
        }
        writeln!(out, "{}", knapsack(&path_items, L)).unwrap();
    }
    out.flush().unwrap();
}

#[allow(unused_must_use)]
mod my {
    pub mod io {
        use std::io::{BufRead, ErrorKind, Result};
        use std::str::{FromStr, from_utf8};
        use std::fmt::Debug;

        pub fn read_word<R: BufRead>(r: &mut R, buf: &mut Vec<u8>)
                                              -> Result<usize> {
            let mut read = 0;
            loop {
                let (done, used) = {
                    let available = match r.fill_buf() {
                        Ok(n) => n,
                        Err(ref e) if e.kind() == ErrorKind::Interrupted => continue,
                        Err(e) => return Err(e)
                    };
                    match available.iter().position(|&x| x == b'\n' || x == b' ') {
                        Some(i) => {
                            buf.extend_from_slice(&available[..i]);
                            (true, i + 1)
                        }
                        None => {
                            buf.extend_from_slice(available);
                            (false, available.len())
                        }
                    }
                };
                r.consume(used);
                read += used;
                if done || used == 0 {
                    return Ok(read);
                }
            }
        }

        pub struct InputReader<R: BufRead> {
            reader: R,
            buf: Vec<u8>,
        }

        impl<R: BufRead> InputReader<R> {
            pub fn new(reader: R) -> InputReader<R> {
                InputReader {
                    reader: reader,
                    buf: Vec::<u8>::new(),
                }
            }

            pub fn read_word(&mut self) {
                read_word(&mut self.reader, &mut self.buf);
            }
            
            pub fn read<T>(&mut self) -> T
                where T: FromStr,
                      T::Err: Debug
            {
                self.buf.clear();
                self.read_word();
                from_utf8(&self.buf).unwrap().trim().parse().unwrap()
            }
        }
    }
}