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.

3
1 2
2 3
3 4
3
1 1
2 5
3 5

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 $3$.

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

256
255
250
247
255
259
223
253