#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")


// [0, n), 0 <= n <= 2^(6D)
template <int D> struct Set {
  int n;
  vector<unsigned long long> a[D];
  explicit Set(int n_ = 0) : n(n_) {
    static_assert(1 <= D && D <= 6, "Set: 1 <= D <= 6 must hold");
    assert(0 <= n); assert(n <= 1LL << (6 * D));
    int m = n ? n : 1;
    for (int d = 0; d < D; ++d) {
      m = (m + 63) >> 6;
      a[d].assign(m, 0);
    }
  }
  bool empty() const {
    return !a[D - 1][0];
  }
  bool contains(int x) const {
    return (a[0][x >> 6] >> (x & 63)) & 1;
  }
  void insert(int x) {
    for (int d = 0; d < D; ++d) {
      const int q = x >> 6, r = x & 63;
      a[d][q] |= 1ULL << r;
      x = q;
    }
  }
  void erase(int x) {
    for (int d = 0; d < D; ++d) {
      const int q = x >> 6, r = x & 63;
      if ((a[d][q] &= ~(1ULL << r))) break;
      x = q;
    }
  }
  // min s.t. >= x
  int next(int x) const {
    for (int d = 0; d < D; ++d) {
      const int q = x >> 6, r = x & 63;
      if (static_cast<unsigned>(q) >= a[d].size()) break;
      const unsigned long long upper = a[d][q] >> r;
      if (upper) {
        x += __builtin_ctzll(upper);
        for (int e = d - 1; e >= 0; --e) x = x << 6 | __builtin_ctzll(a[e][x]);
        return x;
      }
      x = q + 1;
    }
    return n;
  }
  // max s.t. <= x
  int prev(int x) const {
    for (int d = 0; d < D; ++d) {
      if (x < 0) break;
      const int q = x >> 6, r = x & 63;
      const unsigned long long lower = a[d][q] << (63 - r);
      if (lower) {
        x -= __builtin_clzll(lower);
        for (int e = d - 1; e >= 0; --e) x = x << 6 | (63 - __builtin_clzll(a[e][x]));
        return x;
      }
      x = q - 1;
    }
    return -1;
  }
};

////////////////////////////////////////////////////////////////////////////////


int N, TP;
vector<int> A, B;
vector<Int> X;


namespace brute {
vector<vector<int>> graph;
int dist[1010][1010];
void dfs(int r, int u, int p, int d) {
  dist[r][u] = d;
  for (const int v : graph[u]) if (p != v) {
    dfs(r, v, u, d + 1);
  }
}

vector<pair<int, Int>> run() {
cerr<<"[brute::run]"<<endl;
  graph.assign(N, {});
  for (int i = 0; i < N - 1; ++i) {
    graph[A[i]].push_back(B[i]);
    graph[B[i]].push_back(A[i]);
  }
  for (int r = 0; r < N; ++r) {
    dfs(r, r, -1, 0);
  }
  vector<int> on(N, 1);
  vector<Int> freq(N, 0);
  for (int u = 0; u < N; ++u) for (int v = u + 1; v < N; ++v) {
    ++freq[dist[u][v]];
  }
  vector<pair<int, Int>> ans(N - 2);
  Int lastans = 0;
  for (int q = 0; q < N - 2; ++q) {
    const int U = (X[q] ^ (lastans * TP)) - 1;
    assert(on[U]);
    on[U] = 0;
    for (int v = 0; v < N; ++v) if (on[v]) {
      --freq[dist[U][v]];
    }
    for (int d = 1; d < N; ++d) if (freq[d]) {
      ans[q] = make_pair(d, freq[d]);
      break;
    }
    lastans = ans[q].second;
  }
  return ans;
}
}  // brute


namespace chain {
vector<vector<int>> graph;
int dist[1010][1010];
void dfs(int r, int u, int p, int d) {
  dist[r][u] = d;
  for (const int v : graph[u]) if (p != v) {
    dfs(r, v, u, d + 1);
  }
}

vector<pair<int, Int>> run() {
cerr<<"[chain::run]"<<endl;
  vector<pair<int, Int>> ans(N - 2);
  Int lastans = 0;
  Set<4> on(N);
  for (int u = 0; u < N; ++u) {
    on.insert(u);
  }
  map<int, Int> freq;
  freq[1] = N - 1;
  for (int q = 0; q < N - 2; ++q) {
    const int U = (X[q] ^ (lastans * TP)) - 1;
    assert(on.contains(U));
    on.erase(U);
    const int l = on.prev(U);
    const int r = on.next(U);
    if (0 <= l) --freq[U - l];
    if (r < N) --freq[r - U];
    if (0 <= l && r < N) ++freq[r - l];
    for (auto it = freq.begin(); it->second == 0; it = freq.erase(it)) {}
    ans[q] = *freq.begin();
  }
  return ans;
}
}  // chain


int main() {
  for (; ~scanf("%d%d", &N, &TP); ) {
    A.resize(N - 1);
    B.resize(N - 1);
    for (int i = 0; i < N - 1; ++i) {
      scanf("%d%d", &A[i], &B[i]);
      --A[i];
      --B[i];
    }
    X.resize(N - 2);
    for (int q = 0; q < N - 2; ++q) {
      scanf("%lld", &X[q]);
    }
    
    bool isChain = true;
    for (int i = 0; i < N - 1; ++i) {
      isChain = isChain && (A[i] + 1 == B[i]);
    }
    
    vector<pair<int, Int>> ans;
    if (isChain) {
      ans = chain::run();
    } else if (N <= 1000) {
      ans = brute::run();
    } else {
      assert(false);
    }
    for (int q = 0; q < N - 2; ++q) {
      printf("%d %lld\n", ans[q].first, ans[q].second);
    }
  }
  return 0;
}