#include <bits/stdc++.h>
using namespace std;
long long a[1000001];
int nodeNumber[1000001], nodeStart[1000001], nodeEnd[1000001],
    leftStart[1000001], leftEnd[1000001], rightStart[1000001],
    rightEnd[1000001];
void Initialise(int n) {
  sort(a + 1, a + n + 1);
  for (int i = 0; i <= n; ++i) {
    nodeStart[i] = 0;
    nodeEnd[i] = -1;
    nodeNumber[i] = 1;
  }
  nodeStart[1] = 1;
  nodeEnd[1] = n;
}
void FixStartEnd(int &i, int &j) {
  if (i > j) {
    i = 0, j = -1;
  }
}
void FillChildNumbers(int n, int k) {
  for (int i = 0; i <= n; ++i) {
    int j = nodeStart[i];
    for (; j <= nodeEnd[i] && (a[j] & (1ll << k)) == 0; ++j)
      ;
    leftStart[i] = nodeStart[i], leftEnd[i] = j - 1;
    rightStart[i] = j, rightEnd[i] = nodeEnd[i];
    FixStartEnd(leftStart[i], leftEnd[i]);
    FixStartEnd(rightStart[i], rightEnd[i]);
    j = (nodeStart[i] > 0) ? nodeEnd[i] : i;
    nodeStart[i] = 0;
    nodeEnd[i] = -1;
    i = j;
  }
}
long long ZeroBitCount(int n, int k) {
  long long ans = 0;
  for (int i = 1; i <= n; ++i) {
    int targetBit = ((a[i] & (1ll << k)) > 0), j = nodeNumber[i];
    ans += ((targetBit == 1) ? (rightEnd[j] - rightStart[j] + 1)
                             : (leftEnd[j] - leftStart[j] + 1));
  }
  return ans;
}
void TakeZeroBit(int n, int k) {
  for (int i = 1; i <= n; ++i) {
    int targetBit = ((a[i] & (1ll << k)) > 0), j = nodeNumber[i], x, start, end;
    if (targetBit) {
      x = rightStart[j], start = rightStart[j], end = rightEnd[j];
    } else {
      x = leftStart[j], start = leftStart[j], end = leftEnd[j];
    }
    nodeNumber[i] = x, nodeStart[x] = start, nodeEnd[x] = end;
  }
}
void TakeOneBit(int n, int k) {
  for (int i = 1; i <= n; ++i) {
    int targetBit = 1 - ((a[i] & (1ll << k)) > 0), j = nodeNumber[i], x, start,
        end;
    if (targetBit) {
      x = rightStart[j], start = rightStart[j], end = rightEnd[j];
    } else {
      x = leftStart[j], start = leftStart[j], end = leftEnd[j];
    }
    nodeNumber[i] = x, nodeStart[x] = start, nodeEnd[x] = end;
  }
}
int main() {
  int n;
  long long m;
  scanf("%d%lld", &n, &m);
  for (int j = 2; j <= n; ++j) {
    int i;
    long long w;
    scanf("%d%lld", &i, &w);
    a[j] = (w ^ a[i]);
  }
  Initialise(n);
  long long ans = 0;
  for (int k = 61; k > -1; --k) {
    FillChildNumbers(n, k);
    long long cnt = ZeroBitCount(n, k);
    if (cnt >= m) {
      TakeZeroBit(n, k);
    } else {
      ans += (1ll << k);
      m -= cnt;
      TakeOneBit(n, k);
    }
  }
  printf("%lld\n", ans);
  return 0;
}
