#include <bits/stdc++.h>
using namespace std;
template <typename T, typename U>
inline void smin(T &a, U b) {
  if (a > b) a = b;
}
template <typename T, typename U>
inline void smax(T &a, U b) {
  if (a < b) a = b;
}
template <typename T>
inline void gn(T &first) {
  char c, sg = 0;
  while (c = getchar(), (c > '9' || c < '0') && c != '-')
    ;
  for ((c == '-' ? sg = 1, c = getchar() : 0), first = 0; c >= '0' && c <= '9';
       c = getchar())
    first = (first << 1) + (first << 3) + c - '0';
  if (sg) first = -first;
}
template <class T, class T1>
inline void gn(T &first, T1 &second) {
  gn(first);
  gn(second);
}
template <class T, class T1, class T2>
inline void gn(T &first, T1 &second, T2 &z) {
  gn(first);
  gn(second);
  gn(z);
}
template <typename T>
inline void print(T first) {
  if (first < 0) {
    putchar('-');
    return print(-first);
  }
  if (first < 10) {
    putchar('0' + first);
    return;
  }
  print(first / 10);
  putchar(first % 10 + '0');
}
template <typename T>
inline void println(T first) {
  print(first), putchar('\n');
}
template <typename T>
inline void printsp(T first) {
  print(first), putchar(' ');
}
template <class T, class T1>
inline void print(T first, T1 second) {
  printsp(first), println(second);
}
template <class T, class T1, class T2>
inline void print(T first, T1 second, T2 z) {
  printsp(first), printsp(second), println(z);
}
int power(int a, int b, int m, int ans = 1) {
  for (; b; b >>= 1, a = 1LL * a * a % m)
    if (b & 1) ans = 1LL * ans * a % m;
  return ans;
}
int E, head[5050], to[5050], nxt[5050];
void init(int n) {
  E = 0;
  for (int i = 1; i <= n; i++) head[i] = -1;
}
void add_edge(int u, int v) {
  nxt[E] = head[u];
  to[E] = v;
  head[u] = E++;
}
int dp[2][5050][5050], c[5050], d[5050];
int sz[5050];
void dfs(int u) {
  dp[1][u][0] = 0;
  dp[0][u][0] = 0;
  dp[1][u][1] = c[u] - d[u];
  dp[0][u][1] = c[u];
  sz[u] = 1;
  for (int e = head[u]; ~e; e = nxt[e]) {
    int v = to[e];
    dfs(v);
    for (int i = sz[u] + sz[v]; i >= 1; i--) {
      for (int j = min(i, sz[v]); j >= 0 && i - j <= sz[u]; j--) {
        smin(dp[0][u][i], dp[0][u][i - j] + dp[0][v][j]);
        if (i && j < i) smin(dp[1][u][i], dp[1][u][i - j] + dp[1][v][j]);
      }
    }
    sz[u] += sz[v];
  }
  for (int i = 1; i <= sz[u]; i++) smin(dp[1][u][i], dp[0][u][i]);
}
int main() {
  int n, b;
  gn(n, b);
  init(n);
  memset(dp, 0x3f, sizeof(dp));
  for (int i = 1, first; i <= n; i++) {
    gn(c[i], d[i]);
    if (i > 1) {
      gn(first);
      add_edge(first, i);
    }
  }
  dfs(1);
  int ans = 0;
  for (int i = 1; i <= n; i++)
    if (dp[1][1][i] <= b) ans = i;
  println(ans);
  return 0;
}
