#include <bits/stdc++.h>
using namespace std;
template <typename T>
void maxtt(T& t1, T t2) {
  t1 = max(t1, t2);
}
template <typename T>
void mintt(T& t1, T t2) {
  t1 = min(t1, t2);
}
bool debug = 0;
int n, m, k;
int dx[4] = {0, 1, 0, -1}, dy[4] = {1, 0, -1, 0};
string direc = "RDLU";
long long ln, lk, lm;
void etp(bool f = 0) {
  puts(f ? "YES" : "NO");
  exit(0);
}
void addmod(int& x, int y, int mod = 998244353) {
  assert(y >= 0);
  x += y;
  if (x >= mod) x -= mod;
  assert(x >= 0 && x < mod);
}
void et(int x = -1) {
  printf("%d\n", x);
  exit(0);
}
long long fastPow(long long x, long long y, int mod = 998244353) {
  long long ans = 1;
  while (y > 0) {
    if (y & 1) ans = (x * ans) % mod;
    x = x * x % mod;
    y >>= 1;
  }
  return ans;
}
long long gcd1(long long x, long long y) { return y ? gcd1(y, x % y) : x; }
long long w[1000035], ans;
int ch[1000035][2], cnt, pre[1000035], now[1000035], sz[1000035];
int gid(int x, int f) {
  if (ch[x][f] == 0) ch[x][f] = ++cnt;
  return ch[x][f];
}
void fmain(int tid) {
  long long k;
  scanf("%d%lld", &n, &k);
  for (int i = 2; i <= n; i++) {
    int p;
    scanf("%d%lld", &p, w + i);
    w[i] ^= w[p];
  }
  for (int(i) = 1; (i) <= (int)(n); (i)++) pre[i] = now[i] = 1;
  for (int j = 61; ~j; j--) {
    for (int(i) = 1; (i) <= (int)(cnt); (i)++) {
      ch[i][0] = ch[i][1] = 0;
      sz[i] = 0;
    }
    cnt = 0;
    long long ss = 0;
    for (int(i) = 1; (i) <= (int)(n); (i)++) {
      now[i] = gid(now[i], w[i] >> j & 1);
      sz[now[i]]++;
    }
    for (int(i) = 1; (i) <= (int)(n); (i)++) {
      int t = ch[pre[i]][w[i] >> j & 1];
      ss += sz[t];
    }
    int fg = 0;
    if (ss < k) {
      k -= ss;
      ans += 1LL << j;
      fg = 1;
    }
    for (int(i) = 1; (i) <= (int)(n); (i)++)
      pre[i] = ch[pre[i]][(w[i] >> j & 1) ^ fg];
  }
  printf("%lld\n", ans);
}
int main() {
  int t = 1;
  for (int(i) = 1; (i) <= (int)(t); (i)++) {
    fmain(i);
  }
  return 0;
}
