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 Python (3.8.2) (judge verdict: Runtime Error)

N=int(input())
V=[0]
W=[0]
for _ in range(N):
    tmp1,tmp2=map(int,input().split())
    V.append(tmp1)
    W.append(tmp2)
    
Q=int(input())
v=[]
L=[]
for _ in range(N):
    tmp1,tmp2=map(int,input().split())
    v.append(tmp1)
    L.append(tmp2)
#v_は今いる場所
def explorer(V_,W_,v_,L_):
    if v_==1:
        if W_+W[1]<=L_ and V[1]>0:
            return V_+V[1]
        else:
            return V_
    elif W_+W[v_]<=L_ and V[1]>0:
        return max(explorer(V_+V[v_],W_+W[v_],v_//2,L_),explorer(V_,W_,v_//2,L_))
    else:
        return explorer(V_,W_,v_//2,L_)


for i in range(len(L)):
    print(explorer(0,0,v[i],L[i]))