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 PyPy3 (7.3.0) (judge verdict: Time Limit Exceeded)

import bisect
import copy
import heapq
import sys
import itertools
import math
import queue
from functools import lru_cache
input = sys.stdin.readline
sys.setrecursionlimit(1000000)
mod = 10 ** 9 + 7 

def read_values(): return map(int, input().split())
def read_index(): return map(lambda x: int(x) - 1, input().split())
def read_list(): return list(read_values())
def read_lists(N): return [read_list() for n in range(N)]


def make(A, v):
    T = []
    while v != 0:
        T.append(A[v - 1])
        v //= 2

    M = len(T)
    K = []
    for k in range(2 ** M):
        V = 0
        W = 0
        for i in range(M):
            if (k >> i) & 1:
                V += T[i][0]
                W += T[i][1]
            if W > 10 ** 5 + 10:
                break
        
        if W < 10 ** 5 + 10:
            K.append((W, V))
    
    K.sort(key=lambda l: (l[0], -l[1]))

    W2 = [0]
    V2 = [0]
    mv = 0
    for w, v in K:
        if v <= mv:
            continue

        mv = v
        W2.append(w)
        V2.append(mv)

    return (tuple(W2), tuple(V2))

@lru_cache(maxsize=None)
def f(A, v, L):
    T = []
    while v != 0:
        T.append(A[v - 1])
        v //= 2

    M = len(T)
    res = 0
    for k in range(2 ** M):
        V = 0
        W = 0
        for i in range(M):
            if (k >> i) & 1:
                V += T[i][0]
                W += T[i][1]

        if W <= L:
            res = max(res, V)

    return res


P = 8
@lru_cache(maxsize=None)
def f2(A, v, L, V2, W2):
    T = []
    while v >= 2 ** P:
        T.append(A[v - 1])
        v = v >> 1

    M = len(T)
    res = 0
    for k in range(2 ** M):
        V = 0
        W = 0
        for i in range(M):
            if (k >> i) & 1:
                V += T[i][0]
                W += T[i][1]
            if W > L:
                break

        R = L - W
        t = bisect.bisect_right(W2, R)
        res = max(res, V + V2[min(t, len(W2)) - 1])

    return res


def main():
    N = int(input())
    A = []
    for _ in range(N):
        A.append(tuple(read_values()))
    A = tuple(A)
    K = dict()
    Q = int(input())
    ans = [""] * Q
    for q in range(Q):
        v, L = read_values()
        if v.bit_length() <= P:
            ans[q] = str(f(A, v, L))
        else:
            b = v.bit_length()
            v2 = v >> (b - P)
            K2 = K.setdefault(v2, make(A, v2))
            ans[q] = str(f2(A, v, L, K2[1], K2[0]))

    print("\n".join(ans))
    

if __name__ == "__main__":
    main()