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 Ruby (2.7.1) (judge verdict: Time Limit Exceeded)

def answer(target, l, vs, ws)
  dp = Array.new(Math.log2(target).to_i + 2).map{Array.new(l+1, 0)}
  idx = target
  i = 1
  while idx > 0
    dp[i].each_with_index do |_, w|
      if w >= ws[idx-1]
        dp[i][w] = [dp[i-1][w-ws[idx-1]] + vs[idx-1], dp[i-1][w]].max
      else
        dp[i][w] = dp[i-1][w]
      end
    end
    idx /= 2
    i += 1
  end
  dp[-1][-1]
end

def main
  n = gets.to_i
  vs = []
  ws = []
  n.times do
    v,w = gets.chomp.split(" ").map(&:to_i)
    vs.push v
    ws.push w
  end
  q = gets.to_i
  q.times do
    target,l = gets.chomp.split(" ").map(&:to_i)
    puts answer(target, l, vs, ws)
  end
end

main