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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.lang.reflect.Field;
import java.util.Arrays;
import java.util.NoSuchElementException;
import java.util.PrimitiveIterator;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;
import static java.lang.Math.max;




public class Main {
    public static void main(String[] args) throws Exception {
        Field f = System.out.getClass().getDeclaredField("autoFlush");
        f.setAccessible(true);
        f.set(System.out, false);
        execute(System.in, System.out);
    }

    public static void execute(InputStream in, OutputStream out) {
        BasicScanner s = new BasicScanner(System.in);
        Out o = new Out(System.out);
        solve(s, o);
        o.flush();
        o.close();
    }

    public static void solve(BasicScanner sc, Out out) {
        int n = sc.nextInt();
        int[] v = new int[0x40000];
        int[] w = new int[0x40000];
        for (int i = 1; i <= n; i++) {
            v[i] = sc.nextInt();
            w[i] = sc.nextInt();
        }
        int lmax = 100001;
        int[] memo = new int[0x200 * lmax];
        for (int i = 1; i < 0x200; i++) {
            for (int j = 1; j < lmax; j++) {
                if (j >= w[i]) {
                    memo[i * lmax + j] = max(memo[(i >> 1) * lmax + j], memo[(i >> 1) * lmax + j - w[i]] + v[i]);
                } else {
                    memo[i * lmax + j] = memo[(i >> 1) * lmax + j];
                }
                memo[i * lmax + j] = max(memo[i * lmax + j], memo[i * lmax + j - 1]);
            }
        }
        int q = sc.nextInt();
        LongQueue que = new LongQueue(0x200);
        while (q --> 0) {
            int x = sc.nextInt();
            int m = sc.nextInt();
            que.add(0);
            int max = 0;
            for (; x >= 0x200; x >>= 1) {
                int sz = que.size();
                while (sz --> 0) {
                    long vw = que.poll();
                    if ((vw & 0xffff_ffffl) + w[x] <= m) que.add(vw + ((long) v[x] << 32) + w[x]);
                    que.add(vw);
                }
            }
            while (que.size() > 0) {
                long vw = que.poll();
                int vs = (int) (vw >>> 32);
                int ws = (int) (vw & 0xffff_ffffl);
                max = max(max, vs + memo[x * lmax + m - ws]);
            }
            out.write(max).write('\n');
            que.clear();
        }
    }
}


class BasicScanner {
    private final InputStream in;
    private final byte[] buf = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    public BasicScanner(InputStream in) {this.in = in;}
    private boolean hasNextByte() {
        if (ptr < buflen) return true;
        ptr = 0;
        try {buflen = in.read(buf);}
        catch (final IOException e) {e.printStackTrace();}
        return buflen > 0;
    }
    private int readByte() {return hasNextByte() ? buf[ptr++] : -1;}
    public boolean hasNext() {
        while (hasNextByte() && !(33 <= buf[ptr] && buf[ptr] <= 126)) ptr++;
        return hasNextByte();
    }
    private StringBuilder nextSequence() {
        if (!hasNext()) throw new NoSuchElementException();
        final StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (33 <= b && b <= 126) {sb.appendCodePoint(b); b = readByte();}
        return sb;
    }
    public char nextChar() {
        return (char) readByte();
    }
    public String next() {
        return nextSequence().toString();
    }
    public String next(int len) {
        return new String(nextChars(len));
    }
    public char[] nextChars() {
        final StringBuilder sb = nextSequence();
        int l = sb.length();
        char[] dst = new char[l];
        sb.getChars(0, l, dst, 0);
        return dst;
    }
    public char[] nextChars(int len) {
        if (!hasNext()) throw new NoSuchElementException();
        char[] s = new char[len];
        int i = 0;
        int b = readByte();
        while (33 <= b && b <= 126 && i < len) {s[i++] = (char) b; b = readByte();}
        if (i != len) throw new NoSuchElementException(String.format("length %d is longer than the sequence.", len));
        return s;
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {minus = true; b = readByte();}
        if (b < '0' || '9' < b) throw new NumberFormatException();
        while (true) {
            if ('0' <= b && b <= '9') n = n * 10 + b - '0';
            else if (b == -1 || !(33 <= b && b <= 126)) return minus ? -n : n;
            else throw new NumberFormatException();
            b = readByte();
        }
    }
    public int nextInt() {return Math.toIntExact(nextLong());}
    public double nextDouble() {return Double.parseDouble(next());}
}


class Out {
    private final OutputStream out;
    private byte[] buf = new byte[1024];
    private int ptr = 0;
    private static final int AUTO_FLUSH_THRETHOLD = 1 << 17;

    public Out(OutputStream out) {
        this.out = out;
    }

    public void flush() {
        try {
            out.write(buf, 0, ptr);
            out.flush();
            ptr = 0;
        } catch (IOException e) {e.printStackTrace();}
    }

    public void close() {
        try {out.close();} catch (IOException e) {e.printStackTrace();}
    }

    public Out write(Object o) {
        return write(o.toString());
    }

    public Out write(String s) {
        try {
            Field strValueField = s.getClass().getDeclaredField("value");
            strValueField.setAccessible(true);
            byte[] b = (byte[]) strValueField.get(s);
            int l = s.length();
            if (l > AUTO_FLUSH_THRETHOLD) {
                flush();
                int i = 0;
                while (i + AUTO_FLUSH_THRETHOLD < l) {
                    out.write(b, i, AUTO_FLUSH_THRETHOLD);
                    out.flush();
                    i += AUTO_FLUSH_THRETHOLD;
                }
                ensureCapacity(l - i);
                System.arraycopy(b, i, buf, 0, l - i);
                ptr = l - i;
            } else {
                ensureCapacity(ptr + l);
                System.arraycopy(b, 0, buf, ptr, l);
                ptr += l;
            }
        } catch (Exception e) {e.printStackTrace();}
        return this;
    }

    public Out write(char[] c) {
        int l = c.length;
        if (l > AUTO_FLUSH_THRETHOLD) {
            flush();
            ensureCapacity(AUTO_FLUSH_THRETHOLD);
            int i = 0;
            while (i + AUTO_FLUSH_THRETHOLD < l) {
                for (int j = 0; j < AUTO_FLUSH_THRETHOLD; j++) {
                    buf[ptr++] = (byte) c[i + j];
                }
                flush();
                i += AUTO_FLUSH_THRETHOLD;
            }
            for (; i < l; i++) {
                buf[ptr++] = (byte) c[i];
            }
        } else {
            ensureCapacity(ptr + l);
            for (char ch : c) buf[ptr++] = (byte) ch;
        }
        return this;
    }

    public Out write(char c) {
        ensureCapacity(ptr + 1);
        buf[ptr++] = (byte) c;
        return this;
    }

    public Out write(byte b) {
        ensureCapacity(ptr + 1);
        buf[ptr++] = b;
        return this;
    }

    public Out write(int x) {
        if (x == 0) {
            ensureCapacity(ptr + 1);
            buf[ptr++] = '0';
            return this;
        }
        int d = stringSize(x);
        ensureCapacity(ptr + d);
        if (x < 0) {
            buf[ptr++] = '-';
            x = -x;
            d--;
        }
        int j = ptr + d; 
        while (x > 0) {
            buf[--j] = (byte) ('0' + (x % 10));
            x /= 10;
        }
        ptr += d;
        return this;
    }

    public Out write(long x) {
        if (x == 0) {
            ensureCapacity(ptr + 1);
            buf[ptr++] = '0';
            return this;
        }
        int d = stringSize(x);
        ensureCapacity(ptr + d);
        if (x < 0) {
            buf[ptr++] = '-';
            x = -x;
            d--;
        }
        int j = ptr + d; 
        while (x > 0) {
            buf[--j] = (byte) ('0' + (x % 10));
            x /= 10;
        }
        ptr += d;
        return this;
    }

    public Out write(double d) {
        return write(Double.toString(d));
    }

    private void ensureCapacity(int cap) {
        if (cap > AUTO_FLUSH_THRETHOLD) {
            flush();
        }
        if (cap >= buf.length) {
            int newLength = buf.length;
            while (newLength < cap) newLength <<= 1;
            byte[] newBuf = new byte[newLength];
            System.arraycopy(buf, 0, newBuf, 0, buf.length);
            buf = newBuf;
        }
    }
    private static int stringSize(long x) {
        int d = 1;
        if (x >= 0) {d = 0; x = -x;}
        long p = -10;
        for (int i = 1; i < 19; i++, p *= 10) if (x > p) return i + d;
        return 19 + d;
    }
    private static int stringSize(int x) {
        int d = 1;
        if (x >= 0) {d = 0; x = -x;}
        int p = -10;
        for (int i = 1; i < 10; i++, p *= 10) if (x > p) return i + d;
        return 10 + d;
    }
}


/**
 * @author https://atcoder.jp/users/suisen
 */
final class ExtendedScanner extends BasicScanner {
    public ExtendedScanner(InputStream in) {super(in);}
    public int[] ints(final int n) {
        final int[] a = new int[n];
        Arrays.setAll(a, $ -> nextInt());
        return a;
    }
    public int[] ints(final int n, final IntUnaryOperator f) {
        final int[] a = new int[n];
        Arrays.setAll(a, $ -> f.applyAsInt(nextInt()));
        return a;
    }
    public int[][] ints(final int n, final int m) {
        final int[][] a = new int[n][];
        Arrays.setAll(a, $ -> ints(m));
        return a;
    }
    public int[][] ints(final int n, final int m, final IntUnaryOperator f) {
        final int[][] a = new int[n][];
        Arrays.setAll(a, $ -> ints(m, f));
        return a;
    }
    public long[] longs(final int n) {
        final long[] a = new long[n];
        Arrays.setAll(a, $ -> nextLong());
        return a;
    }
    public long[] longs(final int n, final LongUnaryOperator f) {
        final long[] a = new long[n];
        Arrays.setAll(a, $ -> f.applyAsLong(nextLong()));
        return a;
    }
    public long[][] longs(final int n, final int m) {
        final long[][] a = new long[n][];
        Arrays.setAll(a, $ -> longs(m));
        return a;
    }
    public long[][] longs(final int n, final int m, final LongUnaryOperator f) {
        final long[][] a = new long[n][];
        Arrays.setAll(a, $ -> longs(m, f));
        return a;
    }
    public char[][] charArrays(final int n) {
        final char[][] c = new char[n][];
        Arrays.setAll(c, $ -> nextChars());
        return c;
    }
    public char[][] charArrays(final int n, final int m) {
        final char[][] c = new char[n][];
        Arrays.setAll(c, $ -> nextChars(m));
        return c;
    }
    public double[] doubles(final int n) {
        final double[] a = new double[n];
        Arrays.setAll(a, $ -> nextDouble());
        return a;
    }
    public double[][] doubles(final int n, final int m) {
        final double[][] a = new double[n][];
        Arrays.setAll(a, $ -> doubles(m));
        return a;
    }
    public String[] strings(final int n) {
        final String[] s = new String[n];
        Arrays.setAll(s, $ -> next());
        return s;
    }
    public String[] strings(final int n, final int m) {
        final String[] s = new String[n];
        Arrays.setAll(s, $ -> next(m));
        return s;
    }
    public boolean[][] grid(final int h, final int w, final char trueCharacter) {
        final boolean[][] grid = new boolean[h][w];
        for (int i = 0; i < h; i++) {
            final char[] s = nextChars(w);
            for (int j = 0; j < w; j++) grid[i][j] = s[j] == trueCharacter;
        }
        return grid;
    }
}


/**
 * @author https://atcoder.jp/users/suisen
 * 
 * Queue for long type.
 */
final class LongQueue implements Iterable<Long> {
    private static final int DEFAULT_SIZE = 64;
    private long[] q;
    private int head = 0, tail = 0;
    public LongQueue(final int capacity) {this.q = new long[capacity];}
    public LongQueue() {this(DEFAULT_SIZE);}
    public long peek() {
        if (head == tail) throw new NoSuchElementException("No Elements.");
        return q[head];
    }
    public long getFromHead(int index) {
        if (head + index >= tail || index < 0) throw new NoSuchElementException("Index out of bounds.");
        return q[head + index];
    }
    public long getFromTail(int index) {
        if (head + index >= tail || index < 0) throw new NoSuchElementException("Index out of bounds.");
        return q[tail - 1 - index];
    }
    public void add(final long v) {
        if (tail == q.length) grow();
        q[tail++] = v;
    }
    public void add(final long... vals) {for (long v : vals) add(v);}
    public long poll() {
        if (head == tail) throw new NoSuchElementException("No Elements.");
        long ret = q[head++];
        if (head == tail) head = tail = 0;
        return ret;
    }
    public int size() {return tail - head;}
    public void clear() {head = tail = 0;}
    private void grow() {
        final long[] grown = new long[q.length << 1];
        final int len = size();
        System.arraycopy(q, head, grown, 0, len);
        q = grown;
        tail = len;
        head = 0;
    }
    public PrimitiveIterator.OfLong iterator() {return new LongQueueIterator();}
    private class LongQueueIterator implements PrimitiveIterator.OfLong {
        private int i = head;
        public boolean hasNext() {return i < tail;}
        public long nextLong() {return q[i++];}
    }
}