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)

#![allow(non_snake_case)]

use proconio::input;
use proconio::fastout;

type Item = (u64, u64);

fn compare(item1: &Item, item2: &Item) -> bool {
    item1.0 >= item2.0 || item1.1 >= item2.1
}

fn enumerate_items(items: &[Item], capacity: u64) -> Vec<Item> {

    let mut a0: Vec<Item> = vec![(0, 0)];
    for (weight, value) in items {
        let N0: usize = a0.len();
        let mut a1: Vec<Item> = Vec::new();
        for (w0, v0) in &a0 {
            let w1: u64 = w0 + weight;
            if w1 > capacity {
                break;
            }
            let v1: u64 = v0 + value;
            a1.push((w1, v1));
        }
        let N1: usize = a1.len();

        let mut b: Vec<Item> = vec![(0, 0)];
        let mut i0: usize = 1;
        let mut i1: usize = 0;
        loop {
            if i0 == N0 {
                while i1 < N1 {
                    b.push(a1[i1]);
                    i1 += 1;
                }
                break;
            } else if i1 == N1 {
                while i0 < N0 {
                    b.push(a0[i0]);
                    i0 += 1;
                }
                break;
            } else {
                if a0[i0].0 < a1[i1].0 {
                    b.push(a0[i0]);
                    i0 += 1;
                    let b_last = b.last().unwrap();
                    while i1 < N1 && compare(b_last, &a1[i1]) {
                        i1 += 1;
                    }
                } else if a0[i0].0 > a1[i1].0 {
                    b.push(a1[i1]);
                    i1 += 1;
                    let b_last = b.last().unwrap();
                    while i0 < N0 && compare(b_last, &a0[i0]) {
                        i0 += 1;
                    }
                } else {
                    if a0[i0].1 >= a1[i1].1 {
                        b.push(a0[i0]);
                        i0 += 1;
                        i1 += 1;
                        let b_last = b.last().unwrap();
                        while i1 < N1 && compare(b_last, &a1[i1]) {
                            i1 += 1;
                        }
                    } else {
                        b.push(a1[i1]);
                        i1 += 1;
                        i0 += 1;
                        let b_last = b.last().unwrap();
                        while i0 < N0 && compare(b_last, &a0[i0]) {
                            i0 += 1;
                        }
                    }
                }
            }
        }
        a0 = b;
    }
    a0
}

fn knapsack_01_small_items(items: &[Item], capacity: u64) -> u64 {

    let N: usize = items.len();
    let N0: usize = N / 2;

    let a0 = enumerate_items(&items[..N0], capacity);
    let a1 = enumerate_items(&items[N0..], capacity);

    let mut result: u64 = 0;
    let mut j: usize = a1.len() - 1;
    'outer: for (w0, v0) in a0 {
        let res: u64 = capacity - w0;
        while a1[j].0 > res {
            if j == 0 {
                break 'outer;
            }
            j -= 1;
        }
        result = std::cmp::max(result, v0 + a1[j].1);
    }
    result
}

#[fastout]
fn main() {

    input! {
        N: usize,
        v_w: [(u64, u64); N],
        Q: usize,
    }
    let mut items = vec![(0u64, 0u64); N + 1];
    for i in 0..N {
      items[i + 1] = (v_w[i].1, v_w[i].0);
  }
  
    for _ in 0..Q {
        input! {
            mut v: usize,
            L: u64,
        }
        let mut path_items = Vec::<(u64, u64)>::new();
        while v > 0 {
            path_items.push(items[v]);
            v /= 2;
        }
        println!("{}", knapsack_01_small_items(&path_items, L));
    }
}