#include <bits/stdc++.h>
inline long long read() {
  long long x = 0;
  char c = getchar(), f = 1;
  for (; c < '0' || '9' < c; c = getchar())
    if (c == '-') f = -1;
  for (; '0' <= c && c <= '9'; c = getchar()) x = x * 10 + c - '0';
  return x * f;
}
inline void write(long long x) {
  static int buf[20], len;
  len = 0;
  if (x < 0) x = -x, putchar('-');
  for (; x; x /= 10) buf[len++] = x % 10;
  if (!len)
    putchar('0');
  else
    while (len) putchar(buf[--len] + '0');
}
inline void writeln(long long x) {
  write(x);
  putchar('\n');
}
inline void writesp(long long x) {
  write(x);
  putchar(' ');
}
struct edge {
  int to, nxt;
  long long val;
} e[2 * 1000010];
struct Data {
  int l, r, x, y;
};
std::vector<Data> x, t;
long long fir[1000010], a[1000010];
int n, tot;
long long k;
inline void add_edge(int x, int y, long long z) {
  e[tot].to = y;
  e[tot].val = z;
  e[tot].nxt = fir[x];
  fir[x] = tot++;
}
void dfs(int now) {
  for (int i = fir[now]; ~i; i = e[i].nxt) {
    a[e[i].to] = a[now] ^ e[i].val;
    dfs(e[i].to);
  }
}
int main() {
  n = read();
  k = read();
  memset(fir, 255, sizeof(fir));
  tot = 0;
  for (int i = 2; i <= n; i++) {
    long long p = read(), w = read();
    add_edge(p, i, w);
  }
  a[1] = 0;
  dfs(1);
  std::sort(a + 1, a + n + 1);
  long long ans = 0;
  x.push_back((Data){1, n, 1, n});
  for (int j = 61; j >= 0; j--) {
    long long cnt = 0;
    for (int i = 0; i < x.size(); i++) {
      int mid1 = x[i].l, mid2 = x[i].x;
      for (; mid1 <= x[i].r; mid1++)
        if ((a[mid1] >> j) & 1) break;
      --mid1;
      for (; mid2 <= x[i].y; mid2++)
        if ((a[mid2] >> j) & 1) break;
      --mid2;
      cnt += (long long)(mid1 - x[i].l + 1) * (mid2 - x[i].x + 1) +
             (long long)(x[i].r - mid1) * (x[i].y - mid2);
    }
    int flag = 0;
    if (k > cnt) {
      flag = 1;
      ans |= 1ll << j;
      k -= cnt;
    }
    t.clear();
    for (int i = 0; i < x.size(); i++) {
      int mid1 = x[i].l, mid2 = x[i].x;
      for (; mid1 <= x[i].r; mid1++)
        if ((a[mid1] >> j) & 1) break;
      for (; mid2 <= x[i].y; mid2++)
        if ((a[mid2] >> j) & 1) break;
      --mid2;
      --mid1;
      if (!flag) {
        if (x[i].l <= mid1 && x[i].x <= mid2)
          t.push_back((Data){x[i].l, mid1, x[i].x, mid2});
        if (mid1 < x[i].r && mid2 < x[i].y)
          t.push_back((Data){mid1 + 1, x[i].r, mid2 + 1, x[i].y});
      } else {
        if (x[i].l <= mid1 && mid2 < x[i].y)
          t.push_back((Data){x[i].l, mid1, mid2 + 1, x[i].y});
        if (mid1 < x[i].r && x[i].x <= mid2)
          t.push_back((Data){mid1 + 1, x[i].r, x[i].x, mid2});
      }
    }
    x = t;
  }
  writeln(ans);
  return 0;
}
