#include <bits/stdc++.h>
using i64 = long long;
const int mxn = 2e5 + 5;
int n;
std::vector<int> adj[mxn];
int q;
struct Query {
  int k, i;
};
std::vector<Query> qry[mxn];
namespace BRUTE {
const int mxn = 2e3 + 5;
int sz[mxn];
int dp[mxn][mxn];
i64 ans[mxn];
void dfs(int u, int p) {
  sz[u] = 0;
  memset(dp[u], -0x3f, sizeof(dp[u]));
  dp[u][0] = 0;
  for (int v : adj[u]) {
    if (v == p) continue;
    dfs(v, u);
    static int ndp[mxn];
    memset(ndp, -0x3f, sizeof(ndp));
    for (int a = 0; a < (int)(sz[u] + 1); ++a)
      for (int b = 0; b < (int)(sz[v] + 1); ++b) {
        ndp[a + b] = std::max(ndp[a + b], dp[u][a] + dp[v][b]);
      }
    memcpy(dp[u], ndp, sizeof(dp[u]));
    sz[u] += sz[v];
  }
  for (auto Q : qry[u]) {
    ans[Q.i] = -(1LL << 60);
    for (int a = 0; a < (int)(sz[u] + 1); ++a)
      ans[Q.i] = std::max(ans[Q.i], dp[u][a] - 1LL * a * Q.k);
  }
  static int ndp[mxn];
  memset(ndp, -0x3f, sizeof(ndp));
  ndp[0] = std::max(ndp[0], 1);
  for (int a = 0; a < (int)(sz[u] + 1); ++a) {
    ndp[a + 1] = std::max(ndp[a + 1], dp[u][a]);
  }
  memcpy(dp[u], ndp, sizeof(dp[u]));
  sz[u] += 1;
}
}  // namespace BRUTE
namespace UPGRADE {
const int mxn = 2e3 + 5;
struct Hull {
  int x[mxn], y[mxn], sz;
  Hull() { sz = 0; }
  void push_back(int X, int Y) {
    while (sz >= 2 && 1LL * (y[sz - 1] - Y) * (x[sz - 2] - x[sz - 1]) <
                          1LL * (y[sz - 2] - y[sz - 1]) * (x[sz - 1] - X))
      --sz;
    x[sz] = X, y[sz] = Y, ++sz;
  }
};
Hull conv(Hull a, Hull b) {
  int bx = a.x[0] + b.x[0], by = a.y[0] + b.y[0];
  Hull c;
  c.push_back(bx, by);
  for (int i = 1, j = 1; i < a.sz || j < b.sz;) {
    if (i < a.sz && (j == b.sz ||
                     1LL * (a.y[i - 1] - a.y[i]) * (b.x[j - 1] - b.x[j]) <
                         1LL * (b.y[j - 1] - b.y[j]) * (a.x[i - 1] - a.x[i]))) {
      c.push_back(bx += a.x[i] - a.x[i - 1], by += a.y[i] - a.y[i - 1]);
      ++i;
    } else {
      c.push_back(bx += b.x[j] - b.x[j - 1], by += b.y[j] - b.y[j - 1]);
      ++j;
    }
  }
  return c;
}
i64 query(Hull a, int x) {
  int lb = 0, rb = a.sz - 1;
  while (lb < rb) {
    int md = (lb + rb) >> 1;
    if (a.y[md] - a.y[md + 1] < 1LL * x * (a.x[md] - a.x[md + 1]))
      lb = md + 1;
    else
      rb = md;
  }
  return a.y[lb] - 1LL * a.x[lb] * x;
}
int sz[mxn];
Hull dp[mxn];
i64 ans[mxn];
void dfs(int u, int p) {
  sz[u] = 0;
  dp[u].push_back(0, 0);
  for (int v : adj[u]) {
    if (v == p) continue;
    dfs(v, u);
    dp[u] = conv(dp[u], dp[v]);
    sz[u] += sz[v];
  }
  for (auto Q : qry[u]) ans[Q.i] = query(dp[u], Q.k);
  for (int i = 0; i < (int)(dp[u].sz); ++i) dp[u].x[i] += 1;
  dp[u].push_back(0, 1);
  sz[u] += 1;
}
}  // namespace UPGRADE
namespace SOL {
struct Node {
  int dx, dy, sx, sy;
  size_t siz;
  Node *ch[2], *fa;
  Node(int _dx, int _dy) {
    dx = sx = _dx, dy = sy = _dy;
    siz = 1;
    ch[0] = ch[1] = fa = nullptr;
  }
  ~Node() {
    if (ch[0]) delete ch[0];
    if (ch[1]) delete ch[1];
  }
};
using node = Node *;
inline bool comp(node a, node b) {
  return 1LL * a->dy * b->dx < 1LL * b->dy * a->dx;
}
inline void pushup(node x) {
  x->sx = x->dx, x->sy = x->dy, x->siz = 1;
  if (x->ch[0])
    x->sx += x->ch[0]->sx, x->sy += x->ch[0]->sy, x->siz += x->ch[0]->siz;
  if (x->ch[1])
    x->sx += x->ch[1]->sx, x->sy += x->ch[1]->sy, x->siz += x->ch[1]->siz;
}
inline void rotate(node x) {
  node y = x->fa, z = y->fa;
  if (z) z->ch[y == z->ch[1]] = x;
  x->fa = z;
  bool d = x == y->ch[1];
  y->ch[d] = x->ch[d ^ 1];
  if (y->ch[d]) y->ch[d]->fa = y;
  x->ch[d ^ 1] = y;
  y->fa = x;
  pushup(y);
  pushup(x);
}
inline node splay(node x) {
  while (x->fa) {
    node y = x->fa, z = y->fa;
    if (z) rotate((x == y->ch[1]) ^ (y == z->ch[1]) ? x : y);
    rotate(x);
  }
  return x;
}
inline node __insert(node x, node v) {
  if (!x) return v;
  if (comp(x, v))
    x->ch[1] = __insert(x->ch[1], v), x->ch[1]->fa = x;
  else
    x->ch[0] = __insert(x->ch[0], v), x->ch[0]->fa = x;
  pushup(x);
  return x;
}
inline node insert(node x, node v) {
  __insert(x, v);
  return splay(v);
}
inline node merge(node x, node y) {
  if (!x || !y) return x ? x : y;
  if (x->siz < y->siz) std::swap(x, y);
  node ls = y->ch[0], rs = y->ch[1];
  y->ch[0] = y->ch[1] = y->fa = nullptr;
  x = merge(x, ls);
  x = insert(x, y);
  x = merge(x, rs);
  return x;
}
inline void debug(node x) {
  if (!x) return;
  debug(x->ch[0]);
  fprintf(stderr, "(%d, %d)", x->dx, x->dy);
  debug(x->ch[1]);
}
struct Hull {
  int bx, by;
  node dif;
  void push_back(int X, int Y) {
    while (dif) {
      node u = dif;
      while (u->ch[1]) u = u->ch[1];
      dif = splay(u);
      node v = dif->ch[0];
      int xm1 = bx + u->sx, ym1 = by + u->sy;
      int xm2 = bx + (v ? v->sx : 0), ym2 = by + (v ? v->sy : 0);
      if (1LL * (ym1 - Y) * (xm2 - xm1) < 1LL * (ym2 - ym1) * (xm1 - X)) {
        u->ch[0] = nullptr;
        if (v) v->fa = nullptr;
        dif = v;
        delete u;
      } else
        break;
    }
    int xm1 = bx + (dif ? dif->sx : 0);
    int ym1 = by + (dif ? dif->sy : 0);
    node u = new Node(X - xm1, Y - ym1);
    dif = insert(dif, u);
  }
};
Hull conv(Hull a, Hull b) {
  return {a.bx + b.bx, a.by + b.by, merge(a.dif, b.dif)};
}
i64 query(Hull &a, int x) {
  node u = a.dif, v = nullptr;
  int bx = a.bx, by = a.by;
  while (u) {
    v = u;
    if (-u->dy < 1LL * x * -u->dx) {
      if (u->ch[0]) bx += u->ch[0]->sx, by += u->ch[0]->sy;
      bx += u->dx, by += u->dy;
      u = u->ch[1];
    } else {
      u = u->ch[0];
    }
  }
  if (v) a.dif = splay(v);
  return by - 1LL * bx * x;
}
int sz[mxn];
Hull dp[mxn];
i64 ans[mxn];
void dfs(int u, int p) {
  sz[u] = 0;
  dp[u] = {0, 0, nullptr};
  for (int v : adj[u]) {
    if (v == p) continue;
    dfs(v, u);
    dp[u] = conv(dp[u], dp[v]);
    sz[u] += sz[v];
  }
  for (auto Q : qry[u]) ans[Q.i] = query(dp[u], Q.k);
  dp[u].bx += 1;
  dp[u].push_back(0, 1);
  sz[u] += 1;
}
}  // namespace SOL
using namespace SOL;
int main() {
  scanf("%d", &n);
  for (int i = 0; i < (int)(n - 1); ++i) {
    int u, v;
    scanf("%d %d", &u, &v);
    --u, --v;
    adj[u].push_back(v);
    adj[v].push_back(u);
  }
  scanf("%d", &q);
  for (int i = 0; i < (int)(q); ++i) {
    int u, k;
    scanf("%d %d", &u, &k);
    --u;
    qry[u].push_back({k, i});
  }
  dfs(0, -1);
  for (int i = 0; i < (int)(q); ++i) printf("%lld\n", ans[i]);
  return 0;
}

### Prompt

In Cpp, your task is to solve the following problem:

You are given a tree consisting of n vertices. Recall that a tree is an undirected connected acyclic graph. The given tree is rooted at the vertex 1.

You have to process q queries. In each query, you are given a vertex of the tree v and an integer k.

To process a query, you may delete any vertices from the tree in any order, except for the root and the vertex v. When a vertex is deleted, its children become the children of its parent. You have to process a query in such a way that maximizes the value of c(v) - m ⋅ k (where c(v) is the resulting number of children of the vertex v, and m is the number of vertices you have deleted). Print the maximum possible value you can obtain.

The queries are independent: the changes you make to the tree while processing a query don't affect the tree in other queries.

Input

The first line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of vertices in the tree.

Then n-1 lines follow, the i-th of them contains two integers x_i and y_i (1 ≤ x_i, y_i ≤ n; x_i ≠ y_i) — the endpoints of the i-th edge. These edges form a tree.

The next line contains one integer q (1 ≤ q ≤ 2 ⋅ 10^5) — the number of queries.

Then q lines follow, the j-th of them contains two integers v_j and k_j (1 ≤ v_j ≤ n; 0 ≤ k_j ≤ 2 ⋅ 10^5) — the parameters of the j-th query.

Output

For each query, print one integer — the maximum value of c(v) - m ⋅ k you can achieve.

Example

Input


8
6 7
3 2
8 3
5 7
7 4
7 1
7 3
6
1 0
1 2
1 3
7 1
5 0
7 200000


Output


5
2
1
4
0
4

Note

The tree in the first example is shown in the following picture:

<image>

Answers to the queries are obtained as follows:

  1. v=1,k=0: you can delete vertices 7 and 3, so the vertex 1 has 5 children (vertices 2, 4, 5, 6, and 8), and the score is 5 - 2 ⋅ 0 = 5; 
  2. v=1,k=2: you can delete the vertex 7, so the vertex 1 has 4 children (vertices 3, 4, 5, and 6), and the score is 4 - 1 ⋅ 2 = 2. 
  3. v=1,k=3: you shouldn't delete any vertices, so the vertex 1 has only one child (vertex 7), and the score is 1 - 0 ⋅ 3 = 1; 
  4. v=7,k=1: you can delete the vertex 3, so the vertex 7 has 5 children (vertices 2, 4, 5, 6, and 8), and the score is 5 - 1 ⋅ 1 = 4; 
  5. v=5,k=0: no matter what you do, the vertex 5 will have no children, so the score is 0; 
  6. v=7,k=200000: you shouldn't delete any vertices, so the vertex 7 has 4 children (vertices 3, 4, 5, and 6), and the score is 4 - 0 ⋅ 200000 = 4. 

### Response

```cpp
#include <bits/stdc++.h>
using i64 = long long;
const int mxn = 2e5 + 5;
int n;
std::vector<int> adj[mxn];
int q;
struct Query {
  int k, i;
};
std::vector<Query> qry[mxn];
namespace BRUTE {
const int mxn = 2e3 + 5;
int sz[mxn];
int dp[mxn][mxn];
i64 ans[mxn];
void dfs(int u, int p) {
  sz[u] = 0;
  memset(dp[u], -0x3f, sizeof(dp[u]));
  dp[u][0] = 0;
  for (int v : adj[u]) {
    if (v == p) continue;
    dfs(v, u);
    static int ndp[mxn];
    memset(ndp, -0x3f, sizeof(ndp));
    for (int a = 0; a < (int)(sz[u] + 1); ++a)
      for (int b = 0; b < (int)(sz[v] + 1); ++b) {
        ndp[a + b] = std::max(ndp[a + b], dp[u][a] + dp[v][b]);
      }
    memcpy(dp[u], ndp, sizeof(dp[u]));
    sz[u] += sz[v];
  }
  for (auto Q : qry[u]) {
    ans[Q.i] = -(1LL << 60);
    for (int a = 0; a < (int)(sz[u] + 1); ++a)
      ans[Q.i] = std::max(ans[Q.i], dp[u][a] - 1LL * a * Q.k);
  }
  static int ndp[mxn];
  memset(ndp, -0x3f, sizeof(ndp));
  ndp[0] = std::max(ndp[0], 1);
  for (int a = 0; a < (int)(sz[u] + 1); ++a) {
    ndp[a + 1] = std::max(ndp[a + 1], dp[u][a]);
  }
  memcpy(dp[u], ndp, sizeof(dp[u]));
  sz[u] += 1;
}
}  // namespace BRUTE
namespace UPGRADE {
const int mxn = 2e3 + 5;
struct Hull {
  int x[mxn], y[mxn], sz;
  Hull() { sz = 0; }
  void push_back(int X, int Y) {
    while (sz >= 2 && 1LL * (y[sz - 1] - Y) * (x[sz - 2] - x[sz - 1]) <
                          1LL * (y[sz - 2] - y[sz - 1]) * (x[sz - 1] - X))
      --sz;
    x[sz] = X, y[sz] = Y, ++sz;
  }
};
Hull conv(Hull a, Hull b) {
  int bx = a.x[0] + b.x[0], by = a.y[0] + b.y[0];
  Hull c;
  c.push_back(bx, by);
  for (int i = 1, j = 1; i < a.sz || j < b.sz;) {
    if (i < a.sz && (j == b.sz ||
                     1LL * (a.y[i - 1] - a.y[i]) * (b.x[j - 1] - b.x[j]) <
                         1LL * (b.y[j - 1] - b.y[j]) * (a.x[i - 1] - a.x[i]))) {
      c.push_back(bx += a.x[i] - a.x[i - 1], by += a.y[i] - a.y[i - 1]);
      ++i;
    } else {
      c.push_back(bx += b.x[j] - b.x[j - 1], by += b.y[j] - b.y[j - 1]);
      ++j;
    }
  }
  return c;
}
i64 query(Hull a, int x) {
  int lb = 0, rb = a.sz - 1;
  while (lb < rb) {
    int md = (lb + rb) >> 1;
    if (a.y[md] - a.y[md + 1] < 1LL * x * (a.x[md] - a.x[md + 1]))
      lb = md + 1;
    else
      rb = md;
  }
  return a.y[lb] - 1LL * a.x[lb] * x;
}
int sz[mxn];
Hull dp[mxn];
i64 ans[mxn];
void dfs(int u, int p) {
  sz[u] = 0;
  dp[u].push_back(0, 0);
  for (int v : adj[u]) {
    if (v == p) continue;
    dfs(v, u);
    dp[u] = conv(dp[u], dp[v]);
    sz[u] += sz[v];
  }
  for (auto Q : qry[u]) ans[Q.i] = query(dp[u], Q.k);
  for (int i = 0; i < (int)(dp[u].sz); ++i) dp[u].x[i] += 1;
  dp[u].push_back(0, 1);
  sz[u] += 1;
}
}  // namespace UPGRADE
namespace SOL {
struct Node {
  int dx, dy, sx, sy;
  size_t siz;
  Node *ch[2], *fa;
  Node(int _dx, int _dy) {
    dx = sx = _dx, dy = sy = _dy;
    siz = 1;
    ch[0] = ch[1] = fa = nullptr;
  }
  ~Node() {
    if (ch[0]) delete ch[0];
    if (ch[1]) delete ch[1];
  }
};
using node = Node *;
inline bool comp(node a, node b) {
  return 1LL * a->dy * b->dx < 1LL * b->dy * a->dx;
}
inline void pushup(node x) {
  x->sx = x->dx, x->sy = x->dy, x->siz = 1;
  if (x->ch[0])
    x->sx += x->ch[0]->sx, x->sy += x->ch[0]->sy, x->siz += x->ch[0]->siz;
  if (x->ch[1])
    x->sx += x->ch[1]->sx, x->sy += x->ch[1]->sy, x->siz += x->ch[1]->siz;
}
inline void rotate(node x) {
  node y = x->fa, z = y->fa;
  if (z) z->ch[y == z->ch[1]] = x;
  x->fa = z;
  bool d = x == y->ch[1];
  y->ch[d] = x->ch[d ^ 1];
  if (y->ch[d]) y->ch[d]->fa = y;
  x->ch[d ^ 1] = y;
  y->fa = x;
  pushup(y);
  pushup(x);
}
inline node splay(node x) {
  while (x->fa) {
    node y = x->fa, z = y->fa;
    if (z) rotate((x == y->ch[1]) ^ (y == z->ch[1]) ? x : y);
    rotate(x);
  }
  return x;
}
inline node __insert(node x, node v) {
  if (!x) return v;
  if (comp(x, v))
    x->ch[1] = __insert(x->ch[1], v), x->ch[1]->fa = x;
  else
    x->ch[0] = __insert(x->ch[0], v), x->ch[0]->fa = x;
  pushup(x);
  return x;
}
inline node insert(node x, node v) {
  __insert(x, v);
  return splay(v);
}
inline node merge(node x, node y) {
  if (!x || !y) return x ? x : y;
  if (x->siz < y->siz) std::swap(x, y);
  node ls = y->ch[0], rs = y->ch[1];
  y->ch[0] = y->ch[1] = y->fa = nullptr;
  x = merge(x, ls);
  x = insert(x, y);
  x = merge(x, rs);
  return x;
}
inline void debug(node x) {
  if (!x) return;
  debug(x->ch[0]);
  fprintf(stderr, "(%d, %d)", x->dx, x->dy);
  debug(x->ch[1]);
}
struct Hull {
  int bx, by;
  node dif;
  void push_back(int X, int Y) {
    while (dif) {
      node u = dif;
      while (u->ch[1]) u = u->ch[1];
      dif = splay(u);
      node v = dif->ch[0];
      int xm1 = bx + u->sx, ym1 = by + u->sy;
      int xm2 = bx + (v ? v->sx : 0), ym2 = by + (v ? v->sy : 0);
      if (1LL * (ym1 - Y) * (xm2 - xm1) < 1LL * (ym2 - ym1) * (xm1 - X)) {
        u->ch[0] = nullptr;
        if (v) v->fa = nullptr;
        dif = v;
        delete u;
      } else
        break;
    }
    int xm1 = bx + (dif ? dif->sx : 0);
    int ym1 = by + (dif ? dif->sy : 0);
    node u = new Node(X - xm1, Y - ym1);
    dif = insert(dif, u);
  }
};
Hull conv(Hull a, Hull b) {
  return {a.bx + b.bx, a.by + b.by, merge(a.dif, b.dif)};
}
i64 query(Hull &a, int x) {
  node u = a.dif, v = nullptr;
  int bx = a.bx, by = a.by;
  while (u) {
    v = u;
    if (-u->dy < 1LL * x * -u->dx) {
      if (u->ch[0]) bx += u->ch[0]->sx, by += u->ch[0]->sy;
      bx += u->dx, by += u->dy;
      u = u->ch[1];
    } else {
      u = u->ch[0];
    }
  }
  if (v) a.dif = splay(v);
  return by - 1LL * bx * x;
}
int sz[mxn];
Hull dp[mxn];
i64 ans[mxn];
void dfs(int u, int p) {
  sz[u] = 0;
  dp[u] = {0, 0, nullptr};
  for (int v : adj[u]) {
    if (v == p) continue;
    dfs(v, u);
    dp[u] = conv(dp[u], dp[v]);
    sz[u] += sz[v];
  }
  for (auto Q : qry[u]) ans[Q.i] = query(dp[u], Q.k);
  dp[u].bx += 1;
  dp[u].push_back(0, 1);
  sz[u] += 1;
}
}  // namespace SOL
using namespace SOL;
int main() {
  scanf("%d", &n);
  for (int i = 0; i < (int)(n - 1); ++i) {
    int u, v;
    scanf("%d %d", &u, &v);
    --u, --v;
    adj[u].push_back(v);
    adj[v].push_back(u);
  }
  scanf("%d", &q);
  for (int i = 0; i < (int)(q); ++i) {
    int u, k;
    scanf("%d %d", &u, &k);
    --u;
    qry[u].push_back({k, i});
  }
  dfs(0, -1);
  for (int i = 0; i < (int)(q); ++i) printf("%lld\n", ans[i]);
  return 0;
}

```