#include <bits/stdc++.h>
using namespace std;
using ll = long long;
template <class t, class u>
void chmax(t& first, u second) {
  if (first < second) first = second;
}
template <class t, class u>
void chmin(t& first, u second) {
  if (second < first) first = second;
}
template <class t>
using vc = vector<t>;
template <class t>
using vvc = vc<vc<t>>;
using pi = pair<int, int>;
using vi = vc<int>;
template <class t, class u>
ostream& operator<<(ostream& os, const pair<t, u>& p) {
  return os << "{" << p.first << "," << p.second << "}";
}
template <class t>
ostream& operator<<(ostream& os, const vc<t>& v) {
  os << "{";
  for (auto e : v) os << e << ",";
  return os << "}";
}
using uint = unsigned;
using ull = unsigned long long;
template <class t, size_t n>
ostream& operator<<(ostream& os, const array<t, n>& first) {
  return os << vc<t>(first.begin(), first.end());
}
template <int i, class T>
void print_tuple(ostream&, const T&) {}
template <int i, class T, class H, class... Args>
void print_tuple(ostream& os, const T& t) {
  if (i) os << ",";
  os << get<i>(t);
  print_tuple<i + 1, T, Args...>(os, t);
}
template <class... Args>
ostream& operator<<(ostream& os, const tuple<Args...>& t) {
  os << "{";
  print_tuple<0, tuple<Args...>, Args...>(os, t);
  return os << "}";
}
template <class t>
void print(t x, int suc = 1) {
  cout << x;
  if (suc == 1) cout << "\n";
  if (suc == 2) cout << " ";
}
ll read() {
  ll i;
  cin >> i;
  return i;
}
vi readvi(int n, int off = 0) {
  vi v(n);
  for (int i = int(0); i < int(n); i++) v[i] = read() + off;
  return v;
}
template <class T>
void print(const vector<T>& v, int suc = 1) {
  for (int i = int(0); i < int(v.size()); i++)
    print(v[i], i == int(v.size()) - 1 ? suc : 2);
}
string readString() {
  string s;
  cin >> s;
  return s;
}
template <class T>
T sq(const T& t) {
  return t * t;
}
void yes(bool ex = true) {
  cout << "Yes"
       << "\n";
  if (ex) exit(0);
}
void no(bool ex = true) {
  cout << "No"
       << "\n";
  if (ex) exit(0);
}
void possible(bool ex = true) {
  cout << "Possible"
       << "\n";
  if (ex) exit(0);
}
void impossible(bool ex = true) {
  cout << "Impossible"
       << "\n";
  if (ex) exit(0);
}
constexpr ll ten(int n) { return n == 0 ? 1 : ten(n - 1) * 10; }
const ll infLL = LLONG_MAX / 3;
const int inf = INT_MAX / 2 - 100;
int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int botbit(signed first) { return first == 0 ? 32 : __builtin_ctz(first); }
int botbit(ll first) { return first == 0 ? 64 : __builtin_ctzll(first); }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(ll t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }
ll mask(int i) { return (ll(1) << i) - 1; }
bool inc(int first, int second, int c) {
  return first <= second && second <= c;
}
template <class t>
void mkuni(vc<t>& v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());
}
ll rand_int(ll l, ll r) {
  static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
  return uniform_int_distribution<ll>(l, r)(gen);
}
template <class t>
void myshuffle(vc<t>& first) {
  for (int i = int(0); i < int(int(first.size())); i++)
    swap(first[i], first[rand_int(0, i)]);
}
template <class t>
int lwb(const vc<t>& v, const t& first) {
  return lower_bound(v.begin(), v.end(), first) - v.begin();
}
const int nmax = 50010;
const int L = 8;
const int B = 1 << L;
int first[nmax], mx[nmax][nmax / B + 1];
int par[nmax], len[nmax], jp[nmax], dep[nmax];
vi t[nmax];
int dfs(int v, int p, int d) {
  par[v] = p;
  dep[v] = d;
  for (auto c : t[v])
    if (c != p) {
      chmax(len[v], dfs(c, v, d + 1));
    }
  return len[v] + 1;
}
int seg[B * 2];
int getmx(int lv, int i, int x) {
  if (lv == L) return ((x ^ (i - B)) << L) + seg[i];
  for (int w = int(0); w < int(2); w++) {
    int to = i * 2 + (1 ^ ((x >> (L - 1 - lv)) & 1) ^ w);
    if (seg[to] == -1) continue;
    return getmx(lv + 1, to, x);
  }
}
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  cout << fixed << setprecision(20);
  int n, q;
  cin >> n >> q;
  for (int i = int(0); i < int(n); i++) cin >> first[i];
  for (int _ = int(0); _ < int(n - 1); _++) {
    int c, second;
    cin >> c >> second;
    c--;
    second--;
    t[c].push_back(second);
    t[second].push_back(c);
  }
  dfs(0, -1, 0);
  vi ls;
  for (int i = int(0); i < int(n); i++) {
    int cur = i;
    ls.clear();
    for (int _ = int(0); _ < int(B); _++) {
      ls.push_back(cur);
      cur = par[cur];
      if (cur == -1) break;
    }
    jp[i] = cur;
    if (int(ls.size()) < B) continue;
    memset(seg, -1, sizeof(seg));
    for (int j = int(0); j < int(B); j++) {
      int lw = (first[ls[j]] ^ j) & mask(L);
      int up = (first[ls[j]] ^ j) >> L;
      up += B;
      while (up) {
        chmax(seg[up], lw);
        up >>= 1;
      }
    }
    for (int j = int(0); j < int(len[i] / B + 1); j++) {
      mx[i][j] = getmx(0, 1, j);
    }
  }
  for (int _ = int(0); _ < int(q); _++) {
    int u, v;
    cin >> u >> v;
    u--;
    v--;
    int num = dep[v] - dep[u] + 1;
    int ans = 0;
    for (int i = int(0); i < int(num / B); i++) {
      chmax(ans, mx[v][i]);
      v = jp[v];
    }
    int base = num / B * B;
    for (int i = int(0); i < int(num % B); i++) {
      chmax(ans, first[v] ^ (base + i));
      v = par[v];
    }
    print(ans);
  }
}

### Prompt

Your challenge is to write a CPP solution to the following problem:

Lech got into a tree consisting of n vertices with a root in vertex number 1. At each vertex i written integer ai. He will not get out until he answers q queries of the form u v. Answer for the query is maximal value <image> among all vertices i on path from u to v including u and v, where dist(i, v) is number of edges on path from i to v. Also guaranteed that vertex u is ancestor of vertex v. Leha's tastes are very singular: he believes that vertex is ancestor of itself.

Help Leha to get out.

The expression <image> means the bitwise exclusive OR to the numbers x and y.

Note that vertex u is ancestor of vertex v if vertex u lies on the path from root to the vertex v.

Input

First line of input data contains two integers n and q (1 ≤ n ≤ 5·104, 1 ≤ q ≤ 150 000) — number of vertices in the tree and number of queries respectively.

Next line contains n integers a1, a2, ..., an (0 ≤ ai ≤ n) — numbers on vertices.

Each of next n - 1 lines contains two integers u and v (1 ≤ u, v ≤ n) — description of the edges in tree.

Guaranteed that given graph is a tree.

Each of next q lines contains two integers u and v (1 ≤ u, v ≤ n) — description of queries. Guaranteed that vertex u is ancestor of vertex v.

Output

Output q lines — answers for a queries.

Examples

Input

5 3
0 3 2 1 4
1 2
2 3
3 4
3 5
1 4
1 5
2 4


Output

3
4
3


Input

5 4
1 2 3 4 5
1 2
2 3
3 4
4 5
1 5
2 5
1 4
3 3


Output

5
5
4
3

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
template <class t, class u>
void chmax(t& first, u second) {
  if (first < second) first = second;
}
template <class t, class u>
void chmin(t& first, u second) {
  if (second < first) first = second;
}
template <class t>
using vc = vector<t>;
template <class t>
using vvc = vc<vc<t>>;
using pi = pair<int, int>;
using vi = vc<int>;
template <class t, class u>
ostream& operator<<(ostream& os, const pair<t, u>& p) {
  return os << "{" << p.first << "," << p.second << "}";
}
template <class t>
ostream& operator<<(ostream& os, const vc<t>& v) {
  os << "{";
  for (auto e : v) os << e << ",";
  return os << "}";
}
using uint = unsigned;
using ull = unsigned long long;
template <class t, size_t n>
ostream& operator<<(ostream& os, const array<t, n>& first) {
  return os << vc<t>(first.begin(), first.end());
}
template <int i, class T>
void print_tuple(ostream&, const T&) {}
template <int i, class T, class H, class... Args>
void print_tuple(ostream& os, const T& t) {
  if (i) os << ",";
  os << get<i>(t);
  print_tuple<i + 1, T, Args...>(os, t);
}
template <class... Args>
ostream& operator<<(ostream& os, const tuple<Args...>& t) {
  os << "{";
  print_tuple<0, tuple<Args...>, Args...>(os, t);
  return os << "}";
}
template <class t>
void print(t x, int suc = 1) {
  cout << x;
  if (suc == 1) cout << "\n";
  if (suc == 2) cout << " ";
}
ll read() {
  ll i;
  cin >> i;
  return i;
}
vi readvi(int n, int off = 0) {
  vi v(n);
  for (int i = int(0); i < int(n); i++) v[i] = read() + off;
  return v;
}
template <class T>
void print(const vector<T>& v, int suc = 1) {
  for (int i = int(0); i < int(v.size()); i++)
    print(v[i], i == int(v.size()) - 1 ? suc : 2);
}
string readString() {
  string s;
  cin >> s;
  return s;
}
template <class T>
T sq(const T& t) {
  return t * t;
}
void yes(bool ex = true) {
  cout << "Yes"
       << "\n";
  if (ex) exit(0);
}
void no(bool ex = true) {
  cout << "No"
       << "\n";
  if (ex) exit(0);
}
void possible(bool ex = true) {
  cout << "Possible"
       << "\n";
  if (ex) exit(0);
}
void impossible(bool ex = true) {
  cout << "Impossible"
       << "\n";
  if (ex) exit(0);
}
constexpr ll ten(int n) { return n == 0 ? 1 : ten(n - 1) * 10; }
const ll infLL = LLONG_MAX / 3;
const int inf = INT_MAX / 2 - 100;
int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int botbit(signed first) { return first == 0 ? 32 : __builtin_ctz(first); }
int botbit(ll first) { return first == 0 ? 64 : __builtin_ctzll(first); }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(ll t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }
ll mask(int i) { return (ll(1) << i) - 1; }
bool inc(int first, int second, int c) {
  return first <= second && second <= c;
}
template <class t>
void mkuni(vc<t>& v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());
}
ll rand_int(ll l, ll r) {
  static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
  return uniform_int_distribution<ll>(l, r)(gen);
}
template <class t>
void myshuffle(vc<t>& first) {
  for (int i = int(0); i < int(int(first.size())); i++)
    swap(first[i], first[rand_int(0, i)]);
}
template <class t>
int lwb(const vc<t>& v, const t& first) {
  return lower_bound(v.begin(), v.end(), first) - v.begin();
}
const int nmax = 50010;
const int L = 8;
const int B = 1 << L;
int first[nmax], mx[nmax][nmax / B + 1];
int par[nmax], len[nmax], jp[nmax], dep[nmax];
vi t[nmax];
int dfs(int v, int p, int d) {
  par[v] = p;
  dep[v] = d;
  for (auto c : t[v])
    if (c != p) {
      chmax(len[v], dfs(c, v, d + 1));
    }
  return len[v] + 1;
}
int seg[B * 2];
int getmx(int lv, int i, int x) {
  if (lv == L) return ((x ^ (i - B)) << L) + seg[i];
  for (int w = int(0); w < int(2); w++) {
    int to = i * 2 + (1 ^ ((x >> (L - 1 - lv)) & 1) ^ w);
    if (seg[to] == -1) continue;
    return getmx(lv + 1, to, x);
  }
}
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  cout << fixed << setprecision(20);
  int n, q;
  cin >> n >> q;
  for (int i = int(0); i < int(n); i++) cin >> first[i];
  for (int _ = int(0); _ < int(n - 1); _++) {
    int c, second;
    cin >> c >> second;
    c--;
    second--;
    t[c].push_back(second);
    t[second].push_back(c);
  }
  dfs(0, -1, 0);
  vi ls;
  for (int i = int(0); i < int(n); i++) {
    int cur = i;
    ls.clear();
    for (int _ = int(0); _ < int(B); _++) {
      ls.push_back(cur);
      cur = par[cur];
      if (cur == -1) break;
    }
    jp[i] = cur;
    if (int(ls.size()) < B) continue;
    memset(seg, -1, sizeof(seg));
    for (int j = int(0); j < int(B); j++) {
      int lw = (first[ls[j]] ^ j) & mask(L);
      int up = (first[ls[j]] ^ j) >> L;
      up += B;
      while (up) {
        chmax(seg[up], lw);
        up >>= 1;
      }
    }
    for (int j = int(0); j < int(len[i] / B + 1); j++) {
      mx[i][j] = getmx(0, 1, j);
    }
  }
  for (int _ = int(0); _ < int(q); _++) {
    int u, v;
    cin >> u >> v;
    u--;
    v--;
    int num = dep[v] - dep[u] + 1;
    int ans = 0;
    for (int i = int(0); i < int(num / B); i++) {
      chmax(ans, mx[v][i]);
      v = jp[v];
    }
    int base = num / B * B;
    for (int i = int(0); i < int(num % B); i++) {
      chmax(ans, first[v] ^ (base + i));
      v = par[v];
    }
    print(ans);
  }
}

```