/**
 * @file
 * @author n685
 * @brief
 * @date 2023-10-24
 *
 *
 */
#include <bits/stdc++.h>

#ifdef LOCAL
std::ifstream cin;
std::ofstream cout;
using std::cerr;
#else
using std::cin;
using std::cout;
#define cerr                                                                   \
  if (false)                                                                   \
  std::cerr
#endif

#ifdef LOCAL
#include "dd/debug.h"
#else
#define dbg(...) 42
#define dbgR(...) 4242
#define dbgP(...) 420
#define dbgRP(...) 420420
void nline() {}
#endif

template <class Node> struct LSeg {
  using T = typename Node::ValueType;
  using RT = typename Node::RT;
  int h, sz;
  std::vector<Node> val;

  void push(int l, int r) {
    l += sz, r += sz;
    for (int s = h - 1, k = (1 << (h - 1)); s >= 1; --s, k /= 2)
      for (int i = (l >> s); i <= (r >> s); ++i)
        val[i].push(val[2 * i], val[2 * i + 1], k);
  }
  void build(int l, int r) {
    l += sz, r += sz;
    l /= 2, r /= 2;
    for (int k = 2; l >= 1; l /= 2, r /= 2, k *= 2)
      for (int i = l; i <= r; ++i)
        val[i].pull(val[2 * i], val[2 * i + 1]);
  }

  LSeg() {}
  LSeg(int _sz) {
    if (_sz == 1) {
      h = 1;
      sz = 1;
    } else {
      h = std::__lg(_sz - 1) + 2;
      sz = (1 << (h - 1));
    }
    val.resize(2 * sz);
  }
  LSeg(const std::vector<T> &v) : LSeg(static_cast<int>(v.size())) {
    for (int i = 0; i < static_cast<int>(v.size()); ++i)
      val[i + sz] = v[i];
    build(0, sz - 1);
  }

  void upd(int l, int r, const std::function<void(Node &, int)> &f) {
    if (l > r)
      return;
    push(l, l), push(r, r);

    bool cl = false, cr = false;
    int k = 1;
    for (l += sz, r += sz; l <= r; l /= 2, r /= 2, k *= 2) {
      if (cl)
        val[l - 1].pull(val[2 * l - 2], val[2 * l - 1]);
      if (cr)
        val[r + 1].pull(val[2 * r + 2], val[2 * r + 3]);
      if (l % 2 == 1)
        f(val[l++], k), cl = true;
      if (r % 2 == 0)
        f(val[r--], k), cr = true;
    }
    for (--l, ++r; r >= 1; l /= 2, r /= 2) {
      if (cl)
        val[l].pull(val[2 * l], val[2 * l + 1]);
      if (cr && (!cl || l != r))
        val[r].pull(val[2 * r], val[2 * r + 1]);
    }
  }
  void set(int l, int r, T v) {
    upd(l, r, [&v](Node &n, int k) { n.set(v, k); });
  }
  void upd(int l, int r) {
    upd(l, r, [](Node &n, int k) { n.upd(k); });
  }
  RT query(int l, int r) {
    if (l > r)
      return Node::ID;
    push(l, l), push(r, r);

    RT ll = Node::ID, rr = Node::ID;
    for (l += sz, r += sz; l <= r; l /= 2, r /= 2) {
      if (l % 2 == 1)
        ll = Node::comb(val[l++], ll);
      if (r % 2 == 0)
        rr = Node::comb(rr, val[r--]);
    }
    return Node::comb(ll, rr);
  }

  int walkL(int l, int r, const std::function<bool(int64_t)> &c) {
    if (l > r)
      return -1;
    push(l, l);
    l += sz;
    if (c(val[l]))
      return l - sz;

    int ind = -1;
    int s = 1;
    for (; l > 1; l /= 2, s *= 2) {
      if (l % 2 == 0 && c(val[l + 1])) {
        ind = l + 1;
        break;
      }
    }
    if (ind == -1)
      return -1;

    while (ind < sz) {
      val[ind].push(val[2 * ind], val[2 * ind + 1], s);
      if (c(val[2 * ind]))
        ind = 2 * ind;
      else if (c(val[2 * ind + 1]))
        ind = 2 * ind + 1;
      else
        return -1;
      s /= 2;
    }
    if (c(val[ind]) && ind - sz <= r)
      return ind - sz;
    else
      return -1;
  }
  int walkR(int l, int r, const std::function<bool(int64_t)> &c) {
    if (l > r)
      return -1;
    push(r, r);
    r += sz;
    if (c(val[r]))
      return r - sz;

    int ind = -1;
    int s = 1;
    for (; r > 1; r /= 2, s *= 2) {
      if (r % 2 == 1 && c(val[r - 1])) {
        ind = r - 1;
        break;
      }
    }
    if (ind == -1)
      return -1;

    while (ind < sz) {
      val[ind].push(val[2 * ind], val[2 * ind + 1], s);
      if (c(val[2 * ind + 1]))
        ind = 2 * ind + 1;
      else if (c(val[2 * ind]))
        ind = 2 * ind;
      else
        return -1;
      s /= 2;
    }
    if (c(val[ind]) && ind - sz >= l)
      return ind - sz;
    else
      return -1;
  }
};
template <class T> struct NodeMax {
  using ValueType = T;
  using RT = T;
  static constexpr RT ID = (RT)-1e9;
  static constexpr T ID2 = (T)-1e9;
  T val = 0;
  T ls = ID2;
  NodeMax() {}
  NodeMax(T v) : val(v) {}
  operator RT() { return val; }
  static RT comb(RT a, RT b) { return std::max(a, b); }
  void set(T v, [[maybe_unused]] int k) {
    val = std::max(val, v);
    ls = std::max(ls, v);
  }
  void pull(NodeMax &ll, NodeMax &rr) {
    if (ls != ID2)
      return;
    val = std::max(ll.val, rr.val);
  }
  void push(NodeMax &ll, NodeMax &rr, int k) {
    if (ls == ID2) {
      return;
    } else {
      ll.set(ls, k / 2);
      rr.set(ls, k / 2);
    }
    ls = ID2;
  }
};
template <class T> struct NodeMin {
  using ValueType = T;
  using RT = T;
  static constexpr RT ID = (RT)1e9;
  static constexpr T ID2 = (T)1e9;
  T val = 0;
  T ls = ID2;
  NodeMin() {}
  NodeMin(T v) : val(v) {}
  operator RT() { return val; }
  static RT comb(RT a, RT b) { return std::min(a, b); }
  void set(T v, [[maybe_unused]] int k) {
    val = std::min(val, v);
    ls = std::min(ls, v);
  }
  void pull(NodeMin &ll, NodeMin &rr) {
    if (ls != ID2)
      return;
    val = std::min(ll.val, rr.val);
  }
  void push(NodeMin &ll, NodeMin &rr, int k) {
    if (ls == ID2) {
      return;
    } else {
      ll.set(ls, k / 2);
      rr.set(ls, k / 2);
    }
    ls = ID2;
  }
};
using Vec = std::array<int64_t, 2>;
using Mat = std::array<Vec, 2>;
const Mat I = {Vec{1, 0}, {0, 1}};
Vec operator+(Vec a, Vec b) { return Vec{a[0] + b[0], a[1] + b[1]}; }
Mat operator*(Mat a, Mat b) {
  Mat ans{};
  for (int i = 0; i < 2; ++i) {
    for (int j = 0; j < 2; ++j)
      for (int k = 0; k < 2; ++k)
        ans[i][j] += a[i][k] * b[k][j];
  }
  return ans;
}
Vec operator*(Mat a, Vec b) {
  Vec ans{};
  for (int i = 0; i < 2; ++i)
    for (int k = 0; k < 2; ++k)
      ans[i] += a[i][k] * b[k];
  return ans;
}
template <class T> struct Node2 {
  using ValueType = T;
  using RT = T;
  static constexpr RT ID = 0;
  // T val = 0;
  Vec val{};
  Mat l = I;
  Node2() {}
  Node2(T v) : val{v, 0} {}
  operator RT() { return val[1]; }
  static RT comb(RT a, RT b) { return a + b; }
  void updM(Mat m, int k) {
    val = m * val;
    l = m * l;
  }
  void upd(int k) { updM(Mat{Vec{1, 0}, {1, 1}}, k); }
  void set(T v, int k) {
    // k is here for debugging purposes
    assert(k == 1);
    val[0] = v;
  }
  void pull(Node2 &ll, Node2 &rr) {
    if (l != I)
      return;
    val = ll.val + rr.val;
  }
  void push(Node2 &ll, Node2 &rr, int k) {
    if (l == I) {
      return;
    } else {
      ll.updM(l, k / 2);
      rr.updM(l, k / 2);
    }
    l = I;
  }
};

int main() {
#ifdef LOCAL
  cin.open("input.txt");
  cout.rdbuf()->pubsetbuf(0, 0);
  cout.open("output.txt");
#else
  cin.tie(nullptr)->sync_with_stdio(false);
#endif

  int n, m;
  cin >> n >> m;

  std::vector<int> a(n);
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
    a[i]--;
  }
  int rt = a[0];
  std::vector<std::vector<int>> adj(n);
  for (int i = 1; i < n; ++i) {
    int f;
    cin >> f;
    --f;
    adj[a[f]].push_back(a[i]);
  }

  LSeg<NodeMin<int>> rr(n);
  for (int i = 0; i < n; ++i)
    rr.val[i + rr.sz] = NodeMin<int>(n - 1);
  rr.build(0, n - 1);

  std::vector<std::vector<int>> add(n), rem(n);
  auto dfs = [&](auto &self, int node) -> std::set<int> * {
    if ((int)adj[node].size() == 0)
      return new std::set<int>{node};
    std::set<int> *mx = nullptr;
    std::vector<std::set<int> *> rest;
    for (int i : adj[node]) {
      std::set<int> *p = self(self, i);
      if (!mx || (int)p->size() > (int)mx->size()) {
        if (mx)
          rest.push_back(mx);
        mx = p;
      } else {
        rest.push_back(p);
      }
    }

    for (auto &s : rest) {
      for (int u : *s) {
        auto it = mx->upper_bound(u);
        if (it != mx->end() && std::next(it) != mx->end()) {
          int v = *std::next(it);
          if (node < u) {
            // rectangle: (node, u], [v, n]
            dbg(node + 1, u, v, n - 1);
            rr.set(node + 1, u, v - 1);
          } else if (v < node) {
            // rectangle: [1, u], [v, node)
            dbg(0, u, v, node - 1);
            add[v].push_back(u + 1);
            rem[node].push_back(u + 1);
          }
        }
        if (it != mx->begin()) {
          int v = *std::prev(it);
          if (node < v) {
            // rectangle: (node, v], [u, n]
            dbg(node + 1, v, u, n - 1);
            rr.set(node + 1, v, u - 1);
          } else if (u < node) {
            // rectangle: [1, v], [u, node)
            dbg(0, v, u, node - 1);
            add[u].push_back(v + 1);
            rem[node].push_back(v + 1);
          }
        }
      }
      mx->merge(*s);
    }

    mx->insert(node);
    return mx;
  };
  dfs(dfs, rt);
  rr.push(0, n - 1);
  std::vector<std::vector<int>> mx(n + 1), mi(n);
  for (int i = 0; i < n; ++i) {
    // ans += std::max(0, (int)rr.val[i + rr.sz] - (int)ll.val[i + ll.sz] + 1);
    assert((int)rr.val[i + rr.sz] >= i);
    mx[(int)rr.val[i + rr.sz] + 1].push_back(i);
    mi[i].push_back(i);
  }
  std::vector<int64_t> ans(m);
  std::vector<std::vector<std::pair<int, int>>> q(n);
  for (int i = 0; i < m; ++i) {
    int l, r;
    cin >> l >> r;
    l--, r--;
    q[r].emplace_back(l, i);
  }

  LSeg<Node2<int64_t>> seg(n);
  std::multiset<int> miX;
  miX.insert(0);
  for (int i = 0; i < n; ++i) {
    for (int j : mx[i])
      seg.set(j, j, 0);
    for (int j : mi[i])
      seg.set(j, j, 1);
    for (int j : rem[i])
      miX.erase(miX.find(j));
    for (int j : add[i])
      miX.insert(j);
    if (*miX.rbegin() < n)
      seg.upd(*miX.rbegin(), n - 1);
    for (auto [l, ind] : q[i])
      ans[ind] = seg.query(l, i);
  }
  for (auto &v : ans)
    cout << v << '\n';
}