#include <stdio.h>
#include <stdlib.h>
#define N 200000
#define log(x) 31 - __builtin_clz(x)

static int B;
int n, mask[N], first[N<<1], niv[N<<1],
  seg[log(N/(log(N) >> 1))+2][N], v[(N<<1)+1], size;

int cmp (int a, int b) {
  return niv[v[a]] < niv[v[b]] ? a : b;
}

int trans (int x, int base = B) {
  return x - (log(mask[x] & ((1 << base) - 1)));
}

int query (int x, int y) {
  if (y - x + 1 <= B)
    return v[trans(y, y-x+1)];
  int ans = cmp(trans(x + B - 1), trans(y));

  x /= B; ++x;
  y /= B; --y;
  if (x <= y) {
    int lg = log(y-x+1);
    ans = cmp(ans, cmp(seg[lg][x], seg[lg][y - (1<<lg) + 1]));
  }
  return v[ans];
}

struct nod {
  int inf;
  struct nod* urm;
} *G[N+1];

void add (int x, int i) {
  struct nod *e = (struct nod*) malloc(sizeof (struct nod));
  e->inf = i;
  e->urm = G[x];

  G[x] = e;
}

void dfs (int x, int from = 0) {
  v[size++] = x;

  struct nod* p = G[x];
  for (; p; p=p->urm)
    if (p->inf != from) {
      first[p->inf] = size;
      dfs(p->inf, x);
    }
  v[size++] = from;
}

int main (void) {
  freopen("lca.in", "r", stdin);
  freopen("lca.out", "w", stdout);

  int q, i, j;
  scanf("%d%d", &n, &q);
  B = log(n) >> 1;
  for (i=2; i<=n; ++i) {
    scanf("%d", &j);
    niv[i] = niv[j] + 1;
    add(j, i);
  }
  dfs(1);

  n = size;
  int at = 0;
  for (i=0; i<n; ++i) {
    at = (at << 1) & ((1<<B) - 1);
    while (at && cmp(i, i - __builtin_ctz(at)) == i)
      at ^= at & -at;
    at |= 1;
    mask[i] = at;
  }

  n /= B;
  for (i=0; i<n; ++i)
    seg[0][i] = trans(B*i + B - 1);

  for (i=1; (1<<i) <= n; ++i)
    for (j=0; j + (1<<i) <= n; ++j)
      seg[i][j] = cmp(seg[i-1][j], seg[i-1][j + (1<<i-1)]);

  int x, y, ans;
  for (; q; --q) {
    scanf("%d%d", &x, &y);
    x = first[x];
    y = first[y];
    if (x > y) {
      i = x;
      x = y;
      y = i;
    }

    ans = query(x, y);
    printf("%d\n", ans);
  }
  return 0;
}