#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }
template <class T>
using V = vector<T>;
template <class T>
using VV = V<V<T>>;
using PV = pair<V<ll>, V<ll>>;
ll solve(V<ll> vl, V<ll> vr, ll k) {
  V<int> pl = {0, int(vl.size())};
  V<int> pr = {0, int(vr.size())};
  ll ans = 0;
  V<ll> nvl, nvr;
  V<int> npl, npr;
  V<ll> buf00, buf01, buf10, buf11;
  for (int ph = 62; ph >= 0; ph--) {
    int n = int(pl.size()) - 1;
    ll lw_sm = 0;
    for (int i = 0; i < n; i++) {
      ll c00 = 0, c01 = 0, c10 = 0, c11 = 0;
      for (int j = pl[i]; j < pl[i + 1]; j++) {
        ll d = vl[j];
        if (d & (1LL << ph))
          c01++;
        else
          c00++;
      }
      for (int j = pr[i]; j < pr[i + 1]; j++) {
        ll d = vr[j];
        if (d & (1LL << ph))
          c11++;
        else
          c10++;
      }
      lw_sm += c00 * c10 + c01 * c11;
    }
    bool nx_lw = k < lw_sm;
    nvl.clear();
    nvr.clear();
    npl.clear();
    npl.push_back(0);
    npr.clear();
    npr.push_back(0);
    for (int i = 0; i < n; i++) {
      buf00.clear();
      buf01.clear();
      buf10.clear();
      buf11.clear();
      for (int j = pl[i]; j < pl[i + 1]; j++) {
        ll d = vl[j];
        bool g = (d & (1LL << ph)) != 0;
        if (g)
          buf00.push_back(d);
        else
          buf01.push_back(d);
      }
      for (int j = pr[i]; j < pr[i + 1]; j++) {
        ll d = vr[j];
        bool g = (d & (1LL << ph)) != 0;
        if (!nx_lw) g = !g;
        if (g)
          buf10.push_back(d);
        else
          buf11.push_back(d);
      }
      if (buf00.size() && buf10.size()) {
        nvl.insert(nvl.end(), buf00.begin(), buf00.end());
        nvr.insert(nvr.end(), buf10.begin(), buf10.end());
        npl.push_back(int(nvl.size()));
        npr.push_back(int(nvr.size()));
      }
      if (buf01.size() && buf11.size()) {
        nvl.insert(nvl.end(), buf01.begin(), buf01.end());
        nvr.insert(nvr.end(), buf11.begin(), buf11.end());
        npl.push_back(int(nvl.size()));
        npr.push_back(int(nvr.size()));
      }
    }
    swap(vl, nvl);
    swap(vr, nvr);
    swap(pl, npl);
    swap(pr, npr);
    if (!nx_lw) {
      ans += (1LL << ph);
      k -= lw_sm;
    }
  }
  return ans;
}
ll rand_int(ll l, ll r) {
  static mt19937 gen(114514);
  return uniform_int_distribution<ll>(l, r)(gen);
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int n;
  ll k;
  cin >> n >> k;
  k--;
  V<ll> w(n);
  w[0] = 0;
  for (int i = 1; i < n; i++) {
    int p;
    ll x;
    p = i - 1;
    cin >> p >> x;
    p--;
    w[i] = w[p] ^ x;
  }
  cout << solve(w, w, k) << endl;
  return 0;
}
