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: Wrong Answer)

import sys,bisect
input=sys.stdin.readline

N=int(input())
vw=[(-1,-1)]
for i in range(N):
    vw.append(tuple(map(int,input().split())))

dp1=[[0,0] for i in range(2**9)]
dp2=[[0,0] for i in range(2**9)]
for _ in range(int(input())):
    v,l=map(int,input().split())
    t=[]
    while v>0:
        t.append(vw[v])
        v//=2
    
    dp1=[[0,0] for i in range(2**9)]
    dp2=[[0,0] for i in range(2**9)]
    n=len(t)
    dp1[0][0]=0
    dp1[0][1]=0
    k=n//2
    for i in range(1,2**k):
        m=i.bit_length()
        dp1[i][0]=dp1[i-2**(m-1)][0]+t[m-1][1]
        dp1[i][1]=dp1[i-2**(m-1)][1]+t[m-1][0]

    dp2[0][0]=0
    dp2[0][1]=0
    for i in range(1,2**(n-k)):
        m=i.bit_length()
        dp2[i][0]=dp2[i-2**(m-1)][0]+t[m-1+k][1]
        dp2[i][1]=dp2[i-2**(m-1)][1]+t[m-1+k][0]

    dp1.sort()
    dp2.sort()
    ans=0
    for i in range(0,2**9):
        res=dp1[i][1]
        id=bisect.bisect_right(dp2,[l-dp1[i][0],10**20])
        if id!=0:
            res+=dp2[id-1][1]
            ans=max(ans,res)
    print("ANS")
    print(ans)