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 Lua (LuaJIT 2.1.0) (judge verdict: Time Limit Exceeded)

local bls, brs = bit.lshift, bit.rshift
local mmi, mma = math.min, math.max
local n = io.read("*n")
local v, w = {}, {}
for i = 1, n do
  v[i], w[i] = io.read("*n", "*n")
end
local head_tbl = {}
local box = {}
local ten5 = 100000
for i = 256, mmi(n, 1023) do
  head_tbl[i - 255] = {}
  local tbl = head_tbl[i - 255]
  for j = 1, ten5 do
    tbl[j] = 0
  end
  for j = 1, 1023 do
    local tmpi, tmpj = i, j
    local weight, val = 0, 0
    for k = 1, 10 do
      if tmpj % 2 == 1 then
        val = val + v[tmpi]
        weight = weight + w[tmpi]
      end
      tmpi = brs(tmpi, 1)
      tmpj = brs(tmpj, 1)
      if tmpi == 0 then break end
    end
    if 0< weight and weight <= ten5 then
      tbl[weight] = mma(tbl[weight], val)
    end
  end
  for i = 2, ten5 do
    tbl[i] = mma(tbl[i], tbl[i - 1])
  end
end
local function debug(...)
  -- print(...)
end
local function output(z)
  print(z)
end

debug(os.clock(), collectgarbage("count"))
local q = io.read("*n")
for iq = 1, q do
  if iq % 1000 == 0 then
    debug(iq, os.clock())
  end
  local pos, wlim = io.read("*n", "*n")
  local deg = 0
  do
    local tmp = pos
    while 0 < tmp do
      deg, tmp = deg + 1, brs(tmp, 1)
    end
  end
  if pos < 256 then
    local ans = 0
    local tot = bls(1, deg)
    for j = 0, tot - 1 do
      local tmpi, tmpj = pos, j
      local val, weight = 0, 0
      for k = 1, deg do
        if tmpj % 2 == 1 then
          val, weight = val + v[tmpi], weight + w[tmpi]
        end
        tmpi, tmpj = brs(tmpi, 1), brs(tmpj, 1)
      end
      if weight <= wlim then
        ans = mma(ans, val)
      end
    end
    output(ans)
  elseif pos < 1024 then
    output(head_tbl[pos - 255][wlim])
  else
    deg = deg - 10
    local basepos = pos
    for i = 1, deg do
      basepos = brs(basepos, 1)
    end
    local tbl = head_tbl[basepos - 255]
    local ans = tbl[wlim]
    local tot = bls(1, deg)
    for j = 1, tot - 1 do
      local tmpi, tmpj = pos, j
      local val, weight = 0, 0
      for k = 1, deg do
        if tmpj % 2 == 1 then
          val, weight = val + v[tmpi], weight + w[tmpi]
        end
        tmpi, tmpj = brs(tmpi, 1), brs(tmpj, 1)
      end
      if weight <= wlim then
        ans = mma(ans, val)
      end
      if weight < wlim then
        ans = mma(ans, val + tbl[wlim - weight])
      end
    end
    output(ans)
  end
end
debug(os.clock())