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 Java (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.math.BigInteger;
import java.util.*;
import java.util.stream.Collectors;

public class Main {
  static final BigInteger TWO = new BigInteger("2");
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    BigInteger n = new BigInteger(sc.next());
    Map<BigInteger, Item> map = new HashMap<>();
    for (BigInteger i = BigInteger.ONE; i.compareTo(n) <= 0; i = i.add(BigInteger.ONE)) {
      int v = sc.nextInt();
      int w = sc.nextInt();
      map.put(i, new Item(v, w));
    }
    int q = sc.nextInt();
    for (int i = 0; i < q; i++) {
      BigInteger v = new BigInteger(sc.next());
      int l = sc.nextInt();
      System.out.println(culc(map, v, l).one());
    }
  }

  static Map<BigInteger, Map<Integer, Tuple<Integer, Integer>>> acc = new HashMap<>();

  static Tuple<Integer, Integer> culc(Map<BigInteger, Item> map, BigInteger v, int l) {
    Map<Integer, Tuple<Integer, Integer>> integerTupleMap = acc.computeIfAbsent(v, k -> new HashMap<>());
    return integerTupleMap.computeIfAbsent(l, k -> {
          Item item = map.get(v);
          if (v.compareTo(BigInteger.ONE) == 0) {
            return item.w() <= l ? new Tuple<>(item.v(), item.w()) : new Tuple<>(0, 0);
          }
          BigInteger parent = v.divide(TWO);
          Tuple<Integer, Integer> tmp = culc(map, parent, l);
          if (item.w() <= l) {
            Tuple<Integer, Integer> t = culc(map, parent, l - item.w());
            t = new Tuple<>(t.one() + item.v(), t.two() + item.w());
            if (t.one() > tmp.one()) {
              tmp = t;
            }
          }
          for (int i = tmp.two(), len = l - 1; i < len; i++) {
            integerTupleMap.put(i, tmp);
          }
          return tmp;
        });
  }
}

class Item {
  int _v;
  int _w;
  Item(int v, int w) {
    _v = v;
    _w = w;
  }
  public int v() {
    return _v;
  }
  public int w() {
    return _w;
  }
}
class Tuple<V, W> {
  V _v;
  W _w;
  Tuple(V v, W w) {
    _v = v;
    _w = w;
  }
  public V one() {
    return _v;
  }
  public W two() {
    return _w;
  }
}