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 competitive::prelude::*;

fn main() {
    input! {
        n: usize,
        vw: [(i32, i32); n],
        q: usize,
        qs: [(Usize1, i32); q],
    }

    let limit = 1 << 10;

    let mut cache = vec![vec![]; limit];

    for v0 in 0..min(n, limit) {
        let mut v = v0;
        let mut items = vec![];

        loop {
            items.push(vw[v]);

            if v == 0 {
                break;
            }

            v = (v - 1) / 2;
        }

        let mut t = power_set(&items);
        t.sort();
        let mut maxv = 0;

        for i in 0..t.len() {
            maxv = max(maxv, t[i].1);
            t[i].1 = maxv;
        }

        cache[v0] = t;
    }

    for (mut v, l) in qs {
        let mut a = vec![];

        while v >= limit {
            a.push(vw[v]);
            v = (v - 1) / 2;
        }

        let c = &cache[v];

        let mut ans = 0;

        for bs in power_bitset(a.len()) {
            let mut v = 0;
            let mut w = 0;
            for i in 0..a.len() {
                if bs[i] {
                    v += a[i].0;
                    w += a[i].1;
                }
            }

            let rest = l - w;
            if rest < 0 {
                continue;
            }

            let t = binary_search(0, c.len(), |i| c[i].0 <= rest);
            ans = max(ans, c[t].1 + v);
        }

        echo!(ans);
    }
}

fn power_set(x: &[(i32, i32)]) -> Vec<(i32, i32)> {
    let mut ret = vec![];
    let n = x.len();

    for b in power_bitset(n) {
        let mut v = 0;
        let mut w = 0;
        for i in 0..n {
            if b[i] {
                v += x[i].0;
                w += x[i].1;
            }
        }

        ret.push((w, v));
    }
    ret
}
*/

fn main() {
    let exe = "/tmp/bin2DC5C96C";
    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>";