#include <bits/stdc++.h>
using namespace std;
const int MAXN = 100005;
const int INF = 0x3f3f3f3f;
int n, Q;
int Read() {
  int x = 0, f = 1;
  char c = getchar();
  while (c > '9' || c < '0') {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    x = (x * 10) + (c ^ 48);
    c = getchar();
  }
  return x * f;
}
void Put1(int x) {
  if (x > 9) Put1(x / 10);
  putchar(x % 10 ^ 48);
}
void Put(int x, char c = -1) {
  if (x < 0) putchar('-'), x = -x;
  Put1(x);
  if (c >= 0) putchar(c);
}
template <typename T>
T Max(T x, T y) {
  return x > y ? x : y;
}
template <typename T>
T Min(T x, T y) {
  return x < y ? x : y;
}
template <typename T>
T Abs(T x) {
  return x < 0 ? -x : x;
}
int head[MAXN], tot;
struct edge {
  int v, nxt;
} e[MAXN];
void Add_Edge(int x, int y) {
  e[++tot].v = y;
  e[tot].nxt = head[x];
  head[x] = tot;
}
int dfn[MAXN], dfntot, f[MAXN][17], d[MAXN], fdfn[MAXN];
void dfs(int x, int fa) {
  d[x] = d[fa] + 1;
  f[x][0] = fa;
  dfn[x] = ++dfntot;
  fdfn[dfntot] = x;
  for (int i = 1; i <= 16; ++i) f[x][i] = f[f[x][i - 1]][i - 1];
  for (int i = head[x]; i; i = e[i].nxt) dfs(e[i].v, x);
}
int lca(int x, int y) {
  if (!x || !y) return x + y;
  if (x == y) return x;
  if (d[x] < d[y]) swap(x, y);
  for (int i = 16; i >= 0; --i)
    if (d[f[x][i]] >= d[y]) x = f[x][i];
  if (x == y) return x;
  for (int i = 16; i >= 0; --i)
    if (f[x][i] != f[y][i]) x = f[x][i], y = f[y][i];
  return f[x][0];
}
struct SegmentTree {
  struct node {
    int l, r, MAX, MIN, LCA;
  } t[MAXN << 2];
  void update(int x) {
    t[x].MAX = Max(t[x << 1].MAX, t[x << 1 | 1].MAX);
    t[x].MIN = Min(t[x << 1].MIN, t[x << 1 | 1].MIN);
    t[x].LCA = lca(t[x << 1].LCA, t[x << 1 | 1].LCA);
  }
  void Build(int x, int l, int r) {
    t[x].l = l;
    t[x].r = r;
    if (l == r) {
      t[x].MAX = t[x].MIN = dfn[l];
      t[x].LCA = l;
      return;
    }
    int mid = (l + r) >> 1;
    Build(x << 1, l, mid);
    Build(x << 1 | 1, mid + 1, r);
    update(x);
  }
  int qmin(int x, int l, int r) {
    if (l <= t[x].l && t[x].r <= r) return t[x].MIN;
    int mid = (t[x].l + t[x].r) >> 1, ret = INF;
    if (l <= mid) ret = Min(ret, qmin(x << 1, l, r));
    if (mid + 1 <= r) ret = Min(ret, qmin(x << 1 | 1, l, r));
    return ret;
  }
  int qmax(int x, int l, int r) {
    if (l <= t[x].l && t[x].r <= r) return t[x].MAX;
    int mid = (t[x].l + t[x].r) >> 1, ret = 0;
    if (l <= mid) ret = Max(ret, qmax(x << 1, l, r));
    if (mid + 1 <= r) ret = Max(ret, qmax(x << 1 | 1, l, r));
    return ret;
  }
  int qlca(int x, int l, int r) {
    if (l > r) return 0;
    if (l <= t[x].l && t[x].r <= r) return t[x].LCA;
    int mid = (t[x].l + t[x].r) >> 1, ret = 0;
    if (l <= mid) ret = qlca(x << 1, l, r);
    if (mid + 1 <= r) ret = lca(ret, qlca(x << 1 | 1, l, r));
    return ret;
  }
} st;
int main() {
  n = Read();
  Q = Read();
  for (int i = 2; i <= n; ++i) Add_Edge(Read(), i);
  dfs(1, 0);
  st.Build(1, 1, n);
  while (Q--) {
    int l = Read(), r = Read();
    int MIN = fdfn[st.qmin(1, l, r)], MAX = fdfn[st.qmax(1, l, r)];
    int MINLCA = lca(st.qlca(1, l, MIN - 1), st.qlca(1, MIN + 1, r)),
        MAXLCA = lca(st.qlca(1, l, MAX - 1), st.qlca(1, MAX + 1, r));
    if (d[MINLCA] > d[MAXLCA])
      Put(MIN, ' '), Put(d[MINLCA] - 1, '\n');
    else
      Put(MAX, ' '), Put(d[MAXLCA] - 1, '\n');
  }
  return 0;
}
