#include <bits/stdc++.h>
#pragma GCC optimize(2, 3, "Ofast", "unroll-loops")
using namespace std;
namespace fast_io {
char buf[1 << 12], *p1 = buf, *p2 = buf, sr[1 << 23], z[23], nc;
int C = -1, Z = 0, Bi = 0, ny;
inline char gc() {
  return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 1 << 12, stdin), p1 == p2)
             ? EOF
             : *p1++;
}
inline long long read() {
  long long x = 0;
  ny = 1;
  while (nc = gc(), (nc < 48 || nc > 57) && nc != EOF)
    if (nc == 45) ny = -1;
  Bi = 1;
  if (nc < 0) return nc;
  x = nc - 48;
  while (nc = gc(), 47 < nc && nc < 58 && nc != EOF)
    x = (x << 3) + (x << 1) + (nc ^ 48), Bi++;
  return x * ny;
}
inline double find() {
  int a = read(), y = ny, b = (nc != '.') ? 0 : read();
  return (b ? a + (double)b / pow(10, Bi) * y : a);
}
inline int gs(char *s) {
  char c, *t = s;
  while (c = gc(), c <= 32)
    ;
  *s++ = c;
  while (c = gc(), c > 32) *s++ = c;
  return s - t;
}
inline void ot() {
  fwrite(sr, 1, C + 1, stdout);
  C = -1;
}
inline void flush() {
  if (C > 1 << 22) ot();
}
template <typename T>
inline void write(T x, char t) {
  int y = 0;
  if (x < 0) y = 1, x = -x;
  while (z[++Z] = x % 10 + 48, x /= 10)
    ;
  if (y) z[++Z] = '-';
  while (sr[++C] = z[Z], --Z)
    ;
  sr[++C] = t;
  flush();
}
inline void write(char *s) {
  int l = strlen(s);
  for (int i = 0; i < l; i++) sr[++C] = *s++;
  sr[++C] = '\n';
  flush();
}
}  // namespace fast_io
using namespace fast_io;
const int N = 1e6 + 5;
int n, a[N], b[N], ch[N][2], siz[N];
long long ans, k, val[N];
int main() {
  n = read(), k = read();
  a[1] = b[1] = 1;
  for (int i = 2, x; i <= n; i++)
    x = read(), val[i] = val[x] ^ read(), a[i] = b[i] = 1;
  for (int i = 61; ~i; i--) {
    int c = 0;
    long long s = 0;
    for (int j = 1; j <= n; j++) ch[j][0] = ch[j][1] = siz[j] = 0;
    for (int j = 1; j <= n; j++) {
      int &p = ch[a[j]][val[j] >> i & 1];
      if (!p) p = ++c;
      siz[a[j] = p]++;
    }
    for (int j = 1; j <= n; j++) s += siz[ch[b[j]][val[j] >> i & 1]];
    int op = 0;
    if (s < k) k -= s, op = 1, ans |= 1ll << i;
    for (int j = 1; j <= n; j++) b[j] = ch[b[j]][val[j] >> i & 1 ^ op];
  }
  write(ans, '\n');
  return ot(), 0;
}
