#include <bits/stdc++.h>
using namespace std;
const int N = 110000;
const int LOGN = 20;
const int oo = 1e9;
const int MOD = 1000000007;
int n, q, dp[N][LOGN], depth[N], seg[4 * N][LOGN], num[N], bk[N], cnt = 1;
vector<int> g[N];
void dfs(int u, int p) {
  dp[u][0] = p;
  num[u] = cnt++;
  bk[cnt - 1] = u;
  for (auto v : g[u]) {
    depth[v] = depth[u] + 1;
    dfs(v, u);
  }
}
void buildLCA() {
  for (int k = 1; k < LOGN; ++k) {
    for (int u = 1; u <= n; ++u) {
      if (dp[u][k - 1] == -1) continue;
      dp[u][k] = dp[dp[u][k - 1]][k - 1];
    }
  }
}
int lca(int u, int v) {
  if (depth[u] > depth[v]) swap(u, v);
  for (int k = LOGN - 1; k >= 0; --k) {
    if (depth[v] - (1 << k) >= depth[u]) v = dp[v][k];
  }
  if (v == u) return v;
  for (int k = LOGN - 1; k >= 0; --k) {
    if (dp[u][k] != dp[v][k]) {
      u = dp[u][k];
      v = dp[v][k];
    }
  }
  return dp[u][0];
}
int get(int type, int n, int s, int e, int l, int r) {
  if (s > r || e < l) return (type ? -oo : oo);
  if (s >= l && e <= r) return seg[n][type];
  if (type) {
    return max(get(type, 2 * n, s, (s + e) / 2, l, r),
               get(type, 2 * n + 1, (s + e) / 2 + 1, e, l, r));
  } else {
    return min(get(type, 2 * n, s, (s + e) / 2, l, r),
               get(type, 2 * n + 1, (s + e) / 2 + 1, e, l, r));
  }
}
void update(int type, int n, int s, int e, int at, int val) {
  if (s > at || e < at) return;
  if (s == e) {
    seg[n][type] = val;
    return;
  }
  update(type, 2 * n, s, (s + e) / 2, at, val);
  update(type, 2 * n + 1, (s + e) / 2 + 1, e, at, val);
  if (type == 0) {
    seg[n][type] = min(seg[2 * n][type], seg[2 * n + 1][type]);
  } else {
    seg[n][type] = max(seg[2 * n][type], seg[2 * n + 1][type]);
  }
}
pair<int, int> get(int l, int r) {
  return make_pair(get(0, 1, 1, n, l, r), get(1, 1, 1, n, l, r));
}
int main() {
  memset(dp, -1, sizeof dp);
  cin >> n >> q;
  for (int p, i = 2; i <= n; ++i) {
    scanf("%d", &p);
    g[p].push_back(i);
  }
  dfs(1, -1);
  buildLCA();
  for (int i = 1; i <= n; ++i) {
    update(0, 1, 1, n, i, num[i]);
    update(1, 1, 1, n, i, num[i]);
  }
  while (q--) {
    int l, r;
    scanf("%d%d", &l, &r);
    int mnIdx = get(0, 1, 1, n, l, r);
    int mxIdx = get(1, 1, 1, n, l, r);
    int bkMn = bk[mnIdx];
    int bkMx = bk[mxIdx];
    update(1, 1, 1, n, bkMn, -oo);
    update(0, 1, 1, n, bkMn, oo);
    pair<int, int> cur = get(l, r);
    pair<int, int> ans =
        make_pair(depth[lca(bk[cur.first], bk[cur.second])], bkMn);
    update(1, 1, 1, n, bkMn, num[bkMn]);
    update(0, 1, 1, n, bkMn, num[bkMn]);
    update(1, 1, 1, n, bkMx, -oo);
    update(0, 1, 1, n, bkMx, oo);
    cur = get(l, r);
    ans = max(ans, make_pair(depth[lca(bk[cur.first], bk[cur.second])], bkMx));
    update(1, 1, 1, n, bkMx, num[bkMx]);
    update(0, 1, 1, n, bkMx, num[bkMx]);
    printf("%d %d\n", ans.second, ans.first);
  }
  return 0;
}
