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, non_snake_case, dead_code, non_upper_case_globals)]
use std::cmp::*;
use std::collections::*;
use std::mem::*;

fn main() {
    let (r, w, e) = (std::io::stdin(), std::io::stdout(), std::io::stderr());
    let mut io = IO::new(r.lock(), w.lock(), e.lock());
    assert_eq!(!0usize, std::usize::MAX); //🙊

    let n: usize = io.read();
    let mut V = Vec::new();
    let mut W = Vec::new();
    // let mut v = Vec::new();
    // let mut w = Vec::new();
    V.push(0);
    W.push(0);
    for _ in 0..n {
        let (vv, ww) = (io.read::<i64>(), io.read::<i64>());
        V.push(vv);
        W.push(ww);
    }
    let mut sms: Vec<Vec<(i64, i64)>> = vec![Vec::new(); 101010];

    for i in 1..(n + 1) {
        let mut iv = Vec::new();
        let mut ni = i;
        let mut items = Vec::new();
        while ni > 0 {
            items.push((W[ni], V[ni]));
            ni /= 2;
        }
        let mut nn = items.len();
        for ii in 0..1 << nn {
            let mut ww = 0;
            let mut vv = 0;
            for jj in 0..nn {
                if ii >> jj & 1 == 1 {
                    vv += items[jj].1;
                    ww += items[jj].0;
                }
            }
            iv.push((ww, vv));
        }
        iv.sort();
        let mut mxv = 0;
        let mut m = 1;
        for kk in 0..1 << nn {
            if iv[m - 1].1 < iv[kk].1 {
                iv[m] = iv[kk];
                m += 1;
            }
        }
        // io.debug(&iv);
        sms[i] = iv;
    }

    let q: usize = io.read();
    for _ in 0..q {
        let (vv, L): (usize, usize) = (io.read(), io.read());
        let tar = &sms[vv];
        let f = tar.lower_bound(&(L as i64, INF));
        io.writeln(if f > 0 { tar[f - 1].1 } else { 0 });
    }
}

static MOD: i64 = 1000000007;
static INF: i64 = std::i64::MAX >> 1;
// IO
use std::io::*;
struct IO<R: Read, W: Write, E: Write> {
    Read: R,
    Write: BufWriter<W>,
    Error: BufWriter<E>,
}
impl<R: Read, W: Write, E: Write> IO<R, W, E> {
    fn new(r: R, w: W, e: E) -> IO<R, W, E> {
        IO {
            Read: r,
            Write: BufWriter::new(w),
            Error: BufWriter::new(e),
        }
    }
    fn read<T>(&mut self) -> T
    where
        T: std::str::FromStr,
    {
        let next: String = self
            .Read
            .by_ref()
            .bytes()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect();
        next.parse().ok().unwrap()
    }
    fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
    fn chari(&mut self) -> Vec<i64> {
        self.chars()
            .iter()
            .map(|&c| (c as u8 - b'0') as i64)
            .collect::<Vec<i64>>()
    }
    fn readn<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read::<T>()).collect::<Vec<_>>()
    }
    fn readmat<T: std::str::FromStr>(&mut self, n: usize, m: usize) -> Vec<Vec<T>> {
        (0..n).map(|_| self.readn(m)).collect()
    }
    fn write<S: ToString>(&mut self, val: S) {
        self.Write.write(val.to_string().as_bytes());
    }
    fn writeln<S: ToString>(&mut self, val: S) {
        self.Write.write(val.to_string().as_bytes());
        self.Write.write(b"\n");
    }
    fn debug<S: std::fmt::Debug>(&mut self, val: S) {
        writeln!(self.Error, "(debug) {:?}", &val);
    }
    fn debug2<S: std::fmt::Debug, T: std::fmt::Debug>(&mut self, val1: S, val2: T) {
        writeln!(self.Error, "(debug2) {:?} -> {:?}", val1, val2);
    }
    fn debug3<S: std::fmt::Debug, T: std::fmt::Debug, U: std::fmt::Debug>(
        &mut self,
        val1: S,
        val2: T,
        val3: U,
    ) {
        writeln!(
            self.Error,
            "(debug3) {:?} -> {:?} -> {:?}",
            val1, val2, val3
        );
    }
}
trait BinarySearch<T> {
    fn lower_bound(&self, x: &T) -> usize;
    fn upper_bound(&self, x: &T) -> usize;
}
impl<T: Ord> BinarySearch<T> for [T] {
    fn lower_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();
        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less => {
                    low = mid + 1;
                }
                Ordering::Equal | Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
    fn upper_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();
        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less | Ordering::Equal => {
                    low = mid + 1;
                }
                Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
}