Problem: 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.

Examples

Input

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


Output

0
3
3


Input

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


Output

256
255
250
247
255
259
223
253

Solution (in JAVA):

Solution:
import static java.lang.Math.max;

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

public class Main {
    static FastScanner fsc;
    static Out out;
    public static void main(String[] args) throws Exception {
        Field f = System.out.getClass().getDeclaredField("autoFlush");
        f.setAccessible(true);
        f.set(System.out, false);
        fsc = new FastScanner();
        out = new Out(System.out);
        solve();
        out.flush();
        out.close();
    }

    public static void solve() {
        int n = fsc.nextInt();
        int[] v = new int[0x40000];
        int[] w = new int[0x40000];
        for (int i = 1; i <= n; i++) {
            v[i] = fsc.nextInt();
            w[i] = fsc.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 = fsc.nextInt();
        FastLongDeque que = new FastLongDeque(0x200);
        while (q --> 0) {
            int x = fsc.nextInt();
            int m = fsc.nextInt();
            que.addLast(0);
            int max = 0;
            for (; x >= 0x200; x >>= 1) {
                int sz = que.size();
                while (sz --> 0) {
                    long vw = que.removeFirst();
                    if ((vw & 0xffff_ffffl) + w[x] <= m) que.addLast(vw + ((long) v[x] << 32) + w[x]);
                    que.addLast(vw);
                }
            }
            while (que.size() > 0) {
                long vw = que.removeFirst();
                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();
        }
    }
}


/**
 * @author https://atcoder.jp/users/suisen
 */
final class In {
    public static final FastScanner fsc = new FastScanner();
    public static int ni() {return fsc.nextInt();}
    public static int[] ni(final int n) {
        final int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = fsc.nextInt();
        return a;
    }
    public static int[] ni(final int n, final IntUnaryOperator f) {
        final int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = f.applyAsInt(fsc.nextInt());
        return a;
    }
    public static int[][] ni(final int n, final int m) {
        final int[][] a = new int[n][m];
        for (int i = 0; i < n; i++) a[i] = ni(m);
        return a;
    }
    public static int[][] ni(final int n, final int m, final IntUnaryOperator f) {
        final int[][] a = new int[n][m];
        for (int i = 0; i < n; i++) a[i] = ni(m, f);
        return a;
    }
    public static long nl() {return fsc.nextLong();}
    public static long[] nl(final int n) {
        final long[] a = new long[n];
        for (int i = 0; i < n; i++) a[i] = fsc.nextLong();
        return a;
    }
    public static long[] nl(final int n, final LongUnaryOperator f) {
        final long[] a = new long[n];
        for (int i = 0; i < n; i++) a[i] = f.applyAsLong(fsc.nextLong());
        return a;
    }
    public static long[][] nl(final int n, final int m) {
        final long[][] a = new long[n][m];
        for (int i = 0; i < n; i++) a[i] = nl(m);
        return a;
    }
    public static long[][] nl(final int n, final int m, final LongUnaryOperator f) {
        final long[][] a = new long[n][m];
        for (int i = 0; i < n; i++) a[i] = nl(m, f);
        return a;
    }
    public static char[] nc() {return fsc.next().toCharArray();}
    public static char[][] nc(final int n) {
        final char[][] c = new char[n][];
        for (int i = 0; i < n; i++) c[i] = nc();
        return c;
    }
    public static double nd() {return fsc.nextDouble();}
    public static double[] nd(final int n) {
        final double[] a = new double[n];
        for (int i = 0; i < n; i++) a[i] = fsc.nextDouble();
        return a;
    }
    public static double[][] nd(final int n, final int m) {
        final double[][] a = new double[n][m];
        for (int i = 0; i < n; i++) a[i] = nd(m);
        return a;
    }
    public static String ns() {return fsc.next();}
    public static String[] ns(final int n) {
        final String[] s = new String[n];
        for (int i = 0; i < n; i++) s[i] = fsc.next();
        return s;
    }
    public static 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 = fsc.next().toCharArray();
            for (int j = 0; j < w; j++) grid[i][j] = s[j] == trueCharacter;
        }
        return grid;
    }
}


final class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) return true;
        ptr = 0;
        try {buflen = in.read(buffer);}
        catch (final IOException e) {e.printStackTrace();}
        return buflen > 0;
    }
    private int readByte() {return hasNextByte() ? buffer[ptr++] : -1;}
    public boolean hasNext() {
        while (hasNextByte() && !(33 <= buffer[ptr] && buffer[ptr] <= 126)) ptr++;
        return hasNextByte();
    }
    public String next() {
        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.toString();
    }
    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();
        for (; ; b = readByte()) {
            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();
        }
    }
    public int nextInt() {return Math.toIntExact(nextLong());}
    public double nextDouble() {return Double.parseDouble(next());}
}


/**
 * @author https://atcoder.jp/users/suisen
 * 
 * Queue for long type.
 */
final class FastLongDeque {
    private static final int DEFAULT_CAPACITY = 64;
    private long[] circularArray;
    private int head;
    private int tail;
    private int len;
    private int mask;
    private int size;
    public FastLongDeque(int capacity) {
        int k = 1; while (k < capacity) k <<= 1;
        this.len = k;
        this.mask = k - 1;
        this.circularArray = new long[k];
        this.head = 0;
        this.tail = 0;
    }
    public FastLongDeque() {
        this(DEFAULT_CAPACITY);
    }
    public void addFirst(long val) {
        if (size == len) grow();
        head = (head - 1 + len) & mask;
        circularArray[head] = val;
        size++;
    }
    public void addLast(long val) {
        if (size == len) grow();
        circularArray[tail] = val;
        tail = (tail + 1) & mask;
        size++;
    }
    public long removeFirst() {
        if (size == 0) throw new NoSuchElementException("Deque is empty.");
        long ret = circularArray[head];
        head = (head + 1) & mask;
        size--;
        return ret;
    }
    public long removeLast() {
        if (size == 0) throw new NoSuchElementException("Deque is empty.");
        tail = (tail - 1 + len) & mask;
        long ret = circularArray[tail];
        size--;
        return ret;
    }
    public long get(int index) {
        if (index < 0 || index >= size) throw new IndexOutOfBoundsException("Index " + index + " out of bounds for length " + size);
        return circularArray[(head + index) & mask];
    }
    public long getFirst() {
        if (size == 0) throw new NoSuchElementException("Deque is empty.");
        return circularArray[head];
    }
    public long getLast() {
        if (size == 0) throw new NoSuchElementException("Deque is empty.");
        return circularArray[(tail - 1 + len) & mask];
    }
    public int size() {
        return size;
    }
    public void clear() {
        head = tail = 0;
    }
    public PrimitiveIterator.OfLong iterator() {
        return new DequeIterator();
    }
    public PrimitiveIterator.OfLong descendingIterator() {
        return new DescendingDequeIterator();
    }
    public long[] toArray() {
        long[] ret = new long[size];
        for (int i = 0; i < size; i++) ret[i] = circularArray[(head + i) & mask];
        return ret;
    }
    public void clear(int newCapacity) {
        int k = 1; while (k < newCapacity) k <<= 1;
        if (k != len) {
            len = k;
            mask = k - 1;
            circularArray = new long[k];
        }
        head = tail = 0;
    }
    private void grow() {
        int len1 = len - head, len2 = len - len1;
        long[] newArray = new long[len << 1];
        System.arraycopy(circularArray, head, newArray, 0, len1);
        System.arraycopy(circularArray, 0, newArray, len1, len2);
        circularArray = newArray;
        len <<= 1;
        mask = len - 1;
        head = 0; tail = size;
    }

    public String toString() {
        StringBuilder sb = new StringBuilder();
        sb.append('[');
        for (int i = 0; i < size; i++) {
            sb.append(circularArray[(head + i) & mask]);
            if (i < size - 1) {
                sb.append(',');
            }
        }
        sb.append(']');
        return sb.toString();
    }

    private class DequeIterator implements PrimitiveIterator.OfLong {
        private int it;
        public boolean hasNext() {return it < size;}
        public long nextLong() {return circularArray[(head + it++) & mask];}
    }
    private class DescendingDequeIterator implements PrimitiveIterator.OfLong {
        private int it = size;
        public boolean hasNext() {return it > 0;}
        public long nextLong() {return circularArray[(head + --it) & mask];}
    }
}


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;
    }
}