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 C (Clang 10.0.0) (judge verdict: Runtime Error)

#define _CRT_SECURE_NO_WARNINGS

#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <inttypes.h>
#include <limits.h>
#include <ctype.h>
#include <stdint.h>
#include <string.h>
#include <wchar.h>
#include <math.h>

#define N_MAX (100)
#define P_MAX (100)
#define DP_ARRAY_SIZE (N_MAX * P_MAX / 32 + 1)

#define MIN(a, b) ((a) < (b) ? (a) : (b))
#define MAX(a, b) ((a) > (b) ? (a) : (b))
#define ABS(a) ((a) < 0 ? -(a) : (a))
#define ABSS(a, b) ((a) > (b) ? (a) - (b) : (b) - (a))
#define SWAP(type, a, b) { const type tmp = a; a = b; b = tmp; }

int compare_sz_asc(const void* a, const void* b) {
    return *((size_t*)a) < *((size_t*)b) ? -1 : 1;
}

int compare_sz_desc(const void* a, const void* b) {
    return *((size_t*)a) > * ((size_t*)b) ? -1 : 1;
}

int compare_i64_asc(const void* a, const void* b) {
    return *((int64_t*)a) < *((int64_t*)b) ? -1 : 1;
}

int compare_i64_desc(const void* a, const void* b) {
    return *((int64_t*)a) > * ((int64_t*)b) ? -1 : 1;
}

int compare_u64_asc(const void* a, const void* b) {
    return *((uint64_t*)a) < *((uint64_t*)b) ? -1 : 1;
}

int compare_u64_desc(const void* a, const void* b) {
    return *((uint64_t*)a) > * ((uint64_t*)b) ? -1 : 1;
}

int compare_c_asc(const void* a, const void* b) {
    return *((char*)a) < *((char*)b) ? -1 : 1;
}

int compare_c_desc(const void* a, const void* b) {
    return *((char*)a) > * ((char*)b) ? -1 : 1;
}

int compare_dp_asc(const void* a, const void* b) {
    return *((double*)a) < *((double*)b) ? -1 : 1;
}

static uint64_t modinvU64(const uint64_t a, const uint64_t m) {
    int64_t aa = (int64_t)a;
    const int64_t mm = (int64_t)m;
    int64_t b = mm;
    int64_t u = 1;
    int64_t v = 0;

    while (b != 0) {
        const int64_t t = aa / b;

        aa -= t * b;
        SWAP(uint64_t, aa, b);
        u -= t * v;
        SWAP(uint64_t, u, v);
    }

    u %= mm;
    if (u < 0) {
        u += m;
    }

    return (uint64_t)u;
}

static size_t powSz(const size_t base, const size_t exp) {
    if (exp == 0) {
        return 1;
    }

    if (exp == 1) {
        return base;
    }

    if (exp % 2 == 0) {
        return powSz(base * base, exp / 2);
    }
    else {
        return base * powSz(base, exp - 1);
    }
}

static uint64_t powU64(const uint64_t base, const uint64_t exp) {
    if (exp == 0) {
        return 1;
    }

    if (exp == 1) {
        return base;
    }

    if (exp % 2 == 0) {
        return powU64(base * base, exp / 2);
    }
    else {
        return base * powU64(base, exp - 1);
    }
}

static uint64_t powU64WMod(const uint64_t base, const uint64_t exp, const uint64_t m) {
    if (exp == 0) {
        return 1;
    }

    if (exp == 1) {
        return base % m;
    }

    if (exp % 2 == 0) {
        return powU64WMod(base * base % m, exp / 2, m);
    }
    else {
        return base * powU64WMod(base, exp - 1, m) % m;
    }
}

static size_t combSz(const size_t n, const size_t r) {
    size_t result = 1;

    for (size_t i = 0; i < r; i++) {
        result *= n - i;
        result /= i + 1;
    }

    return result;
}

static uint64_t combU64(const uint64_t n, const uint64_t r) {
    uint64_t result = 1;

    for (uint64_t i = 0; i < r; i++) {
        result *= n - i;
        result /= i + 1;
    }

    return result;
}

static uint64_t combU64WMod(const uint64_t n, const uint64_t r, const uint64_t m) {
    uint64_t result = 1;
    uint64_t inv = 1;

    for (uint64_t i = 0; i < r; i++) {
        result = result * (n - i) % m;
        inv = inv * (i + 1) % m;
    }

    return result * modinvU64(inv, m) % m;
}

static uint64_t permU64(const uint64_t n) {
    uint64_t result = 1;

    for (uint64_t v = 2; v <= n; v++) {
        result *= v;
    }

    return result;
}

static uint64_t permU64WMod(const uint64_t n, const uint64_t m) {
    uint64_t result = 1;

    for (uint64_t v = 2; v <= n; v++) {
        result *= v;
        result %= m;
    }

    return result;
}

static size_t gcdZu(size_t m, size_t n) {
    size_t temp;

    while (m % n != 0) {
        temp = n;
        n = m % n;
        m = temp;
    }

    return n;
}

static uint64_t gcdU64(uint64_t m, uint64_t n)
{
    uint64_t temp;

    while (m % n != 0) {
        temp = n;
        n = m % n;
        m = temp;
    }

    return n;
}

static uint64_t popcntU64(uint64_t val) {
    uint64_t cnt = 0;

    while (val != 0) {
        if ((val & UINT64_C(0x1)) != 0) {
            cnt++;
        }

        val >>= UINT64_C(0x1);
    }

    return cnt;
}

typedef struct {
    uint64_t val;
}BHeap_Val;

#define BHEAP_VAL_TYPE BHeap_Val

#define BHEAP_INVALID_NODE ((size_t)100000000)

typedef struct {
    BHEAP_VAL_TYPE val;
} BHeap_Node;


struct _BHeap_Ctx {
    size_t size;
    int (*compare)(const BHEAP_VAL_TYPE* parent, const BHEAP_VAL_TYPE* node);
    void(*notifyNodeChange)(const struct _BHeap_Ctx* const ctx, const size_t nodeListSize, const size_t* const nodeList);
    BHeap_Node* node;
};

typedef struct _BHeap_Ctx BHeap_Ctx;

static void bHeap_Init(BHeap_Ctx* const ctx, int(*compare)(const BHEAP_VAL_TYPE* parent, const BHEAP_VAL_TYPE* node), void(*notifyNodeChange)(const BHeap_Ctx* const ctx, const size_t nodeListSize, const size_t* const nodeList), BHeap_Node* const nodes) {
    ctx->size = 0;
    ctx->compare = compare;
    ctx->notifyNodeChange = notifyNodeChange;
    ctx->node = nodes;
}

static void bHeap_Swap(BHeap_Ctx* const ctx, const size_t node0, const size_t node1) {
    const BHEAP_VAL_TYPE tmp = ctx->node[node0].val;
    ctx->node[node0].val = ctx->node[node1].val;
    ctx->node[node1].val = tmp;

    if (ctx->notifyNodeChange != NULL) {
        const size_t nodeList[2] = { node0,node1 };
        ctx->notifyNodeChange(ctx, 2, nodeList);
    }
}

static void bHeap_UpHeap(BHeap_Ctx* const ctx, const size_t nodeIdx) {
    if (nodeIdx == 0) {
        return;
    }

    const size_t parentIdx = (nodeIdx + 1) / 2 - 1;

    const int compareResult = ctx->compare(&(ctx->node[parentIdx].val), &(ctx->node[nodeIdx].val));

    if (0 < compareResult) {
        bHeap_Swap(ctx, nodeIdx, parentIdx);

        if (parentIdx != 0) {
            bHeap_UpHeap(ctx, parentIdx);
        }
    }
}

static void bHeap_DownHeap(BHeap_Ctx* const ctx, const size_t nodeIdx) {
    if (ctx->size - 1 <= nodeIdx) {
        return;
    }

    const size_t leftIdx = 2 * (nodeIdx + 1) - 1;

    if (leftIdx < ctx->size) {
        const int leftResult = ctx->compare(&(ctx->node[nodeIdx].val), &(ctx->node[leftIdx].val));

        size_t swapTarget = leftResult < 0 ? BHEAP_INVALID_NODE : leftIdx;

        const size_t rightIdx = leftIdx + 1;

        if (rightIdx < ctx->size) {
            const int rightResult = ctx->compare(&(ctx->node[nodeIdx].val), &(ctx->node[rightIdx].val));

            if (swapTarget == BHEAP_INVALID_NODE) {
                if (0 < rightResult) {
                    swapTarget = rightIdx;
                }
            }
            else {
                if (0 < rightResult) {
                    const int rightLeftResult = ctx->compare(&(ctx->node[leftIdx].val), &(ctx->node[rightIdx].val));

                    if (0 < rightLeftResult) {
                        swapTarget = rightIdx;
                    }
                }
            }
        }

        if (swapTarget != BHEAP_INVALID_NODE) {
            bHeap_Swap(ctx, nodeIdx, swapTarget);

            bHeap_DownHeap(ctx, swapTarget);
        }
    }
}

static void bHeap_Add(BHeap_Ctx* const ctx, const BHEAP_VAL_TYPE val) {
    ctx->node[ctx->size].val = val;

    ctx->size++;

    if (ctx->notifyNodeChange != NULL) {
        const size_t node = ctx->size - 1;
        ctx->notifyNodeChange(ctx, 1, &node);
    }

    bHeap_UpHeap(ctx, ctx->size - 1);
}

static void bHeap_RemoveTop(BHeap_Ctx* const ctx) {
    if (ctx->size == 0) {
        return;
    }

    if (ctx->size == 1) {
        ctx->size--;
        return;
    }

    ctx->node[0].val = ctx->node[ctx->size - 1].val;

    if (ctx->notifyNodeChange != NULL) {
        const size_t node = 0;
        ctx->notifyNodeChange(ctx, 1, &node);
    }

    ctx->size--;

    bHeap_DownHeap(ctx, 0);
}

static void bHeap_RemoveNode(BHeap_Ctx* const ctx, const size_t node) {
    if (node == ctx->size - 1) {
        ctx->size--;
    }
    else {
        ctx->node[node].val = ctx->node[ctx->size - 1].val;

        ctx->size--;

        if (ctx->notifyNodeChange != NULL) {
            ctx->notifyNodeChange(ctx, 1, &node);
        }

        bHeap_DownHeap(ctx, node);
        bHeap_UpHeap(ctx, node);
    }
}

static BHEAP_VAL_TYPE* bHeap_GetTopVal(const BHeap_Ctx* const ctx) {
    return ctx->size == 0 ? NULL : &(ctx->node[0].val);
}

typedef struct {
    uint64_t cnt;
    size_t* child;
    size_t numChild;
    size_t maxNumChild;
} Tree_Node;

#define TREE_INIT_ALLOC (128)

static Tree_Node tree_Node[200000];

static void tree_Init(const uint64_t N) {
    for (uint64_t i = 0; i < N; i++) {
        tree_Node[i].cnt = 0;
        tree_Node[i].numChild = 0;
        tree_Node[i].child = malloc(sizeof(size_t) * TREE_INIT_ALLOC);
        tree_Node[i].maxNumChild = TREE_INIT_ALLOC;
    }
}

static void tree_AddChild(const size_t parent, const size_t child) {
    if (tree_Node[parent].maxNumChild <= tree_Node[parent].numChild) {
        tree_Node[parent].child = realloc(tree_Node[parent].child, sizeof(size_t) * tree_Node[parent].maxNumChild * 2);
        tree_Node[parent].maxNumChild *= 2;
    }

    tree_Node[parent].child[tree_Node[parent].numChild] = child;
    tree_Node[parent].numChild++;
}

static BHeap_Node BN_Asc[200000];
static BHeap_Node BN_Desc[200000];

static int _bHeap_Compare_Asc(const BHEAP_VAL_TYPE* parent, const BHEAP_VAL_TYPE* node) {
    return parent->val <= node->val ? -1 : 1;
}

static int _bHeap_Compare_Desc(const BHEAP_VAL_TYPE* parent, const BHEAP_VAL_TYPE* node) {
    return parent->val >= node->val ? -1 : 1;
}

static size_t PBHeap_Asc_Idx[200000];
static size_t PBHeap_Desc_Idx[200000];

static void _bHeap_NotifyNodeChange_Asc(const BHeap_Ctx* const ctx, const size_t nodeListSize, const size_t* const nodeList) {
    for (size_t i = 0; i < nodeListSize; i++) {
        PBHeap_Asc_Idx[ctx->node[nodeList[i]].val.val] = nodeList[i];
    }
}

static void _bHeap_NotifyNodeChange_Desc(const BHeap_Ctx* const ctx, const size_t nodeListSize, const size_t* const nodeList) {
    for (size_t i = 0; i < nodeListSize; i++) {
        PBHeap_Desc_Idx[ctx->node[nodeList[i]].val.val] = nodeList[i];
    }
}

#define UF_ROOT ((size_t)10000000)

typedef struct {
    size_t parent;
    uint64_t w;
    uint64_t v;
    uint64_t wSum;
    uint64_t vSum;
} UF_Node;

static UF_Node uf_Node[101];

static size_t uf_GetRoot(const size_t idx) {
    if (uf_Node[idx].parent == UF_ROOT) {
        return idx;
    }

    const size_t root = uf_GetRoot(uf_Node[idx].parent);

    uf_Node[idx].parent = root;

    return root;
}

static void uf_Merge(const size_t a, const size_t b) {
    const size_t aRoot = uf_GetRoot(a);
    const size_t bRoot = uf_GetRoot(b);

    if (aRoot != bRoot) {
        uf_Node[aRoot].parent = bRoot;

        uf_Node[bRoot].wSum += uf_Node[aRoot].wSum;
        uf_Node[bRoot].vSum += uf_Node[aRoot].vSum;
    }
}

static void sha1(const char* str, uint64_t len, uint32_t* hash) {
    if (len == 0) {
        len = (uint64_t)strlen(str);
    }

    uint32_t h[5] = { 0x67452301 ,0xEFCDAB89 ,0x98BADCFE ,0x10325476 ,0xC3D2E1F0 };

    uint32_t w[80];
    for (uint64_t i = 0; i < 16; i++) {
        w[i] = 0;
    }
    for (uint64_t i = 0; i < len; i++) {
        w[i / 4] |= (uint32_t)(str[i]) << ((i % 4) * 8);
    }
    w[15] = (uint32_t)len * 8;

    for (uint64_t i = 16; i < 80; i++) {
        const uint32_t v = w[i - 3] ^ w[i - 8] ^ w[i - 14] ^ w[i - 16];
        w[i] = (v << 1) | (v >> 31);
    }

    uint32_t a = h[0];
    uint32_t b = h[1];
    uint32_t c = h[2];
    uint32_t d = h[3];
    uint32_t e = h[4];

    for (uint64_t i = 0; i < 80; i++) {
        uint32_t f = 0;
        uint32_t k = 0;
        if (i < 20) {
            f = (a & b) | (~b & d);
            k = 0x5A827999;
        }
        else if (i < 40) {
            f = b ^ c ^ d;
            k = 0x6ED9EBA1;
        }
        else if (i < 60) {
            f = (b & c) | (b & d) | (c & d);
            k = 0x8F1BBCDC;
        }
        else {
            f = b ^ c ^ d;
            k = 0xCA62C1D6;
        }

        const uint32_t t = ((a << 5) | (a >> 27)) + f + e + k + w[i];
        e = d;
        d = c;
        c = (b << 30) | (b >> 2);
        b = a;
        a = t;
    }

    h[0] = h[0] + a;
    h[1] = h[1] + b;
    h[2] = h[2] + c;
    h[3] = h[3] + d;
    h[4] = h[4] + e;

    hash[4] = h[0];
    hash[3] = h[1];
    hash[2] = h[2];
    hash[1] = h[3];
    hash[0] = h[4];
}

#define MOD_VAL (UINT64_C(1000000007))

typedef struct {
    uint64_t strListSize;
    char str[10][11];
} HMap;

static HMap hMap[1000000];

typedef struct {
    bool need;
    uint64_t V;
    uint64_t W;
    uint64_t *dp;
} TN;

static TN tn[262144];

static uint64_t v[100000], L[100000];

static void markV(const uint64_t i) {
    tn[i].need = true;
    tn[i].dp = (uint64_t*)malloc(sizeof(uint64_t) * 100001);

    if (0 < i && !tn[(i - 1) / 2].need) {
        markV((i - 1) / 2);
    }
}

static void calcC(const uint64_t i, const uint64_t N) {
    if (!tn[i].need) {
        return;
    }

    if (i == 0) {
        for (uint64_t w = 0; w <= 100000; w++) {
            if (w < tn[i].W) {
                tn[i].dp[w] = 0;
            }
            else {
                tn[i].dp[w] = tn[i].V;
            }
        }
    }
    else {
        for (uint64_t w = 0; w <= 100000; w++) {
            if (w < tn[i].W) {
                tn[i].dp[w] = tn[(i - 1) / 2].dp[w];
            }
            else {
                tn[i].dp[w] = MAX(tn[(i - 1) / 2].dp[w], tn[(i - 1) / 2].dp[w - tn[i].W] + tn[i].V);
            }
        }
    }

    if (2 * i + 1< N) {
        calcC(2 * i + 1, N);
    }

    if (2 * (i + 1) < N) {
        calcC(2 * (i + 1), N);
    }
}

int main(void) {
    uint64_t N, Q;

    scanf("%"PRIu64, &N);
    for (uint64_t i = 0; i < N; i++) {
        scanf("%"PRIu64"%"PRIu64, &tn[i].V, &tn[i].W);

        tn[i].need = false;
        tn[i].dp = NULL;
    }
    scanf("%"PRIu64, &Q);
    for (uint64_t i = 0; i < Q; i++) {
        scanf("%"PRIu64"%"PRIu64, &v[i], &L[i]);
        v[i]--;

        markV(v[i]);
    }

    calcC(0, N);

    for (uint64_t i = 0; i < Q; i++) {
        printf("%"PRIu64"\n", tn[v[i]].dp[L[i]]);
    }

    return 0;
}