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)

fn compute_dp(n: u32, val: &Vec<u32>, wgt: &Vec<u32>) -> Vec<Vec<u32>> {
    let max_l = 100000;
    let max_dp_n = (1 << 10) - 1;
    let dp_n = std::cmp::min(n, max_dp_n) as usize;

    let dp0 = (0..=max_l)
                  .map(|i| if i < wgt[0] { 0 }
                                    else { val[0] }).collect();
    let mut vec: Vec<Vec<u32>> = Vec::new();
    vec.push(dp0);

    (1..dp_n).for_each(|u| {
        let p = (u - 1) / 2;
        let dpu = (0..=max_l)
                  .map(|i| { let ii = i as usize;
                             if i < wgt[u] { vec[p][ii] }
                             else { let jj = (i - wgt[u]) as usize;
                                    std::cmp::max(vec[p][ii],
                                                  vec[p][jj] + val[u]) }
                      }).collect();
        vec.push(dpu) });
    vec
}

fn solve(u: u32, l: u32, dp: &Vec<Vec<u32>>, val: &Vec<u32>, wgt: &Vec<u32>)
   -> u32
{
    let uu = u as usize;
    let ll = l as usize;
    if uu < dp.len() {
        dp[uu][ll]
    } else {
        let p  = (u - 1) / 2;
        let s = solve(p, l, &dp, &val, &wgt);
        if l >= wgt[uu] {
            std::cmp::max(s, val[uu] + solve(p, l - wgt[uu], &dp, &val, &wgt))
        } else {
            s
        }
    }
}


/// Read functions
/// https://qiita.com/penguinshunya/items/cd96803b74635aebefd6

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}

fn read_vec2<T: std::str::FromStr>(n: u32) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}


fn main() {
    let n: u32 = read();
    let val_wgt: Vec<Vec<u32>> = read_vec2(n);

    let mut val: Vec<u32> = Vec::new();
    let mut wgt: Vec<u32> = Vec::new();
    val_wgt.into_iter().for_each(|vw| { val.push(vw[0]); wgt.push(vw[1]) });

    let dp = compute_dp(n, &val, &wgt);

    let q: u32 = read();
    let query: Vec<Vec<u32>> = read_vec2(q);

    query.into_iter().for_each(|ul| {
        let u = ul[0];
        let l = ul[1];
        println!("{}", solve(u - 1, l, &dp, &val, &wgt))
        });
}