#include<bits/stdc++.h>
#define ll long long
#define db double
#define ull unsigned long long
#define pb push_back
#define pii pair<int, int>
#define FR first
#define SE second
using namespace std;
inline int read() {
  int x = 0; bool op = false;
  char c = getchar();
  while(!isdigit(c))op |= (c == '-'), c = getchar();
  while(isdigit(c))x = (x << 1) + (x << 3) + (c ^ 48), c = getchar();
  return op ? -x : x;
}
const int N = 2e5 + 10;
const int INF = 1e9;
int n, m;
int a[N];
vector<int> G[N];
set<int> st[N];
struct SGT1 {
  int mn[N << 2];
  void build(int k, int l, int r) {
    mn[k] = INF;
    if(l == r)return ;
    int mid = l + r >> 1;
    build(k << 1, l, mid); build(k << 1 | 1, mid + 1, r);
    return ;
  }
  void update(int k, int l, int r, int qx, int qy, int w) {
    if(l >= qx && r <= qy)return mn[k] = min(mn[k], w), void();
    int mid = l + r >> 1;
    if(qx <= mid)update(k << 1, l, mid, qx, qy, w);
    if(qy > mid)update(k << 1 | 1, mid + 1, r, qx, qy, w);
    return ;
  }
  void push(int k, int l, int r, int *f, int val = INF) {
    val = min(val, mn[k]);
    if(l == r)return f[l] = val, void();
    int mid = l + r >> 1;
    push(k << 1, l, mid, f, val); push(k << 1 | 1, mid + 1, r, f, val);
    return ;
  }
}T1, T2;
struct SGT2 {
  ll sum1[N << 2];
  int sum2[N << 2], tg[N << 2];
  void mark(int k, int w) {
    sum1[k] += sum2[k] * w;
    tg[k] += w;
    return ;
  }
  void pushdown(int k) {
    if(tg[k] == 0)return ;
    mark(k << 1, tg[k]);
    mark(k << 1 | 1, tg[k]);
    tg[k] = 0;
    return ;
  }
  void pushup(int k) {
    sum1[k] = sum1[k << 1] + sum1[k << 1 | 1];
    sum2[k] = sum2[k << 1] + sum2[k << 1 | 1];
    return ;
  }
  void update(int k, int l, int r, int qx, int qy, int w) {
    if(l >= qx && r <= qy)return mark(k, w), void();
    int mid = l + r >> 1; pushdown(k);
    if(qx <= mid)update(k << 1, l, mid, qx, qy, w);
    if(qy > mid)update(k << 1 | 1, mid + 1, r, qx, qy, w);
    pushup(k);
    return ;
  }
  void update(int k, int l, int r, int x, int w) {
    if(l == r)return sum2[k] += w, void();
    int mid = l + r >> 1; pushdown(k);
    if(x <= mid)update(k << 1, l, mid, x, w);
    else update(k << 1 | 1, mid + 1, r, x, w);
    pushup(k);
    return ;
  }
  ll query(int k, int l, int r, int qx, int qy) {
    if(l >= qx && r <= qy)return sum1[k];
    int mid = l + r >> 1; ll res = 0; pushdown(k);
    if(qx <= mid)res += query(k << 1, l, mid, qx, qy);
    if(qy > mid)res += query(k << 1 | 1, mid + 1, r, qx, qy);
    return res;
  }
}T3;
void merge(int u, int v) {
  if(st[u].size() < st[v].size())swap(st[u], st[v]);
  for(auto x : st[v]) {
    auto it = st[u].lower_bound(x);
    if(x > a[u]) {
      int p3 = (it == st[u].end() ? n + 1 : *it);
      int p2 = (it == st[u].begin() ? 0 : *prev(it));
      T1.update(1, 1, n, max(a[u], p2) + 1, x, p3 - 1);
      if(p2 > a[u] && it != st[u].begin()) {
        it--;
        int p1 = (it == st[u].begin() ? 0 : *prev(it));
        T1.update(1, 1, n, max(a[u], p1) + 1, p2, x - 1);
      }
    }
    else {
      int p2 = (it == st[u].end() ? n + 1 : *it);
      int p1 = (it == st[u].begin() ? 0 : *prev(it));
      T2.update(1, 1, n, x, min(a[u], p2) - 1, -(p1 + 1));
      if(p2 < a[u] && it != st[u].end()) {
        it++;
        int p3 = (it == st[u].end() ? 0 : *it);
        T2.update(1, 1, n, p2, min(a[u], p3) - 1, -(x + 1));
      }
    }
  }
  for(auto x : st[v])st[u].insert(x);
  return ;
}
void dfs(int u) {
  for(int v : G[u])dfs(v), merge(u, v);
  st[u].insert(a[u]);
  return ;
}
int pl[N], pr[N];
ll ans[N];
vector<pii> q[N];
vector<int> del[N];
int main() {
  n = read(); m = read();
  for(int i = 1; i <= n; i++)a[i] = read();
  for(int i = 2; i <= n; i++) {int u = read(); G[u].pb(i);}
  dfs(1);
  T1.build(1, 1, n); T2.build(1, 1, n);
  T1.push(1, 1, n, pl); T2.push(1, 1, n, pr);
  for(int i = 1; i <= n; i++)
    pl[i] = min(pl[i], n), pr[i] = max(-pr[i], 1);
  // for(int i = 1; i <= n; i++)printf("%d ", pl[i]); putchar('\n');
  // for(int i = 1; i <= n; i++)printf("%d ", pr[i]); putchar('\n');
  // fflush(stdout);
  for(int i = 1; i <= n; i++)del[pr[i] - 1].pb(i);
  for(int i = 1; i <= m; i++) {
    int l = read(), r = read();
    q[l].pb({i, r});
  }
  for(int i = n; i; i--) {
    T3.update(1, 1, n, i, 1);
    for(auto r : del[i])T3.update(1, 1, n, r, -1);
    T3.update(1, 1, n, i, pl[i], 1);
    for(auto t : q[i])ans[t.FR] = T3.query(1, 1, n, i, t.SE);
  }
  for(int i = 1; i <= m; i++)printf("%lld\n", ans[i]);
  return 0;
}