#include <bits/stdc++.h>
using namespace std;
int N;
long long K;
const int MAXN = 1e6 + 100;
vector<pair<int, long long> > adj[MAXN];
long long v[MAXN];
void dfsinit(const int& n = 0) {
  for (int i = 0; i < adj[n].size(); i++) {
    v[adj[n][i].first] ^= v[n] xor adj[n][i].second;
    dfsinit(adj[n][i].first);
  }
}
long long P;
struct NOD {
 public:
  long long prefix;
  int len;
  int l, m, r;
  int upd(const int& dl = 0) {
    len += dl;
    int a = l - 1, b = r;
    while (b > a + 1) {
      int c = a + ((b - a) >> 1);
      if ((v[c] >> len) & 1)
        b = c;
      else
        a = c;
    }
    return m = b;
  }
  int c0() { return m - l; }
  int c1() { return r - m; }
  bool operator==(const NOD& o) const {
    return len == o.len and l == o.l and r == o.r;
  }
  bool operator!=(const NOD& o) const { return !(*this == o); }
};
long long C2(const long long& v) { return ((v * (v + 1)) >> 1); }
pair<NOD, NOD> keep[2][MAXN];
int ks[2];
int main() {
  scanf("%d%lld", &N, &K);
  for (int i = 1, x; i < N; i++) {
    long long w;
    scanf("%d%lld", &x, &w);
    adj[--x].push_back({i, w});
  }
  dfsinit();
  P = 0;
  sort(v, v + N);
  bool cur = 0;
  keep[cur][(ks[cur] = 0)++] = {{0, 62, 0, -1, N}, {0, 62, 0, -1, N}};
  for (int i = 61; i >= 0; i--) {
    ks[cur = !cur] = 0;
    long long ct0 = 0;
    for (int j = 0; j < ks[!cur]; j++) {
      keep[!cur][j].first.upd(-1);
      keep[!cur][j].second.upd(-1);
      assert(i == keep[!cur][j].first.len and i == keep[!cur][j].second.len);
      ct0 += static_cast<long long>(keep[!cur][j].first.c0()) *
                 static_cast<long long>(keep[!cur][j].second.c0()) +
             static_cast<long long>(keep[!cur][j].first.c1()) *
                 static_cast<long long>(keep[!cur][j].second.c1());
    }
    ks[cur] = 0;
    if (ct0 < K) {
      K -= ct0;
      P += (1LL << i);
      for (int j = 0; j < ks[!cur]; j++) {
        if (keep[!cur][j].first.c0() > 0 and keep[!cur][j].second.c1() > 0) {
          keep[cur][ks[cur]] =
              make_pair(keep[!cur][j].first, keep[!cur][j].second);
          keep[cur][ks[cur]].first.r = keep[cur][ks[cur]].first.m;
          keep[cur][ks[cur]].second.l = keep[cur][ks[cur]].second.m;
          ks[cur]++;
        }
        if (keep[!cur][j].first.c1() > 0 and keep[!cur][j].second.c0() > 0) {
          keep[cur][ks[cur]] =
              make_pair(keep[!cur][j].first, keep[!cur][j].second);
          keep[cur][ks[cur]].first.l = keep[cur][ks[cur]].first.m;
          keep[cur][ks[cur]].second.r = keep[cur][ks[cur]].second.m;
          ks[cur]++;
        }
      }
    } else {
      for (int j = 0; j < ks[!cur]; j++) {
        if (keep[!cur][j].first.c0() > 0 and keep[!cur][j].second.c0() > 0) {
          keep[cur][ks[cur]] =
              make_pair(keep[!cur][j].first, keep[!cur][j].second);
          keep[cur][ks[cur]].first.r = keep[cur][ks[cur]].first.m;
          keep[cur][ks[cur]].second.r = keep[cur][ks[cur]].second.m;
          ks[cur]++;
        }
        if (keep[!cur][j].first.c1() > 0 and keep[!cur][j].second.c1() > 0) {
          keep[cur][ks[cur]] =
              make_pair(keep[!cur][j].first, keep[!cur][j].second);
          keep[cur][ks[cur]].first.l = keep[cur][ks[cur]].first.m;
          keep[cur][ks[cur]].second.l = keep[cur][ks[cur]].second.m;
          ks[cur]++;
        }
      }
    }
  }
  printf("%lld\n", P);
  return 0;
}
