/*
* Author: Nonoze
* Created: Thursday 31/10/2024
*/
#include <bits/stdc++.h>
using namespace std;
#ifndef _IN_LOCAL
#define dbg(...)
#endif
#define endl '\n'
#define endlfl '\n' << flush
#define quit(x) return (void)(cout << x << endl)
template<typename T> void read(T& x) { cin >> x;}
template<typename T1, typename T2> void read(pair<T1, T2>& p) { read(p.first), read(p.second);}
template<typename T> void read(vector<T>& v) { for (auto& x : v) read(x); }
template<typename T1, typename T2> void read(T1& x, T2& y) { read(x), read(y); }
template<typename T1, typename T2, typename T3> void read(T1& x, T2& y, T3& z) { read(x), read(y), read(z); }
template<typename T1, typename T2, typename T3, typename T4> void read(T1& x, T2& y, T3& z, T4& zz) { read(x), read(y), read(z), read(zz); }
template<typename T> void print(vector<T>& v) { for (auto& x : v) cout << x << ' '; cout << endl; }
#define sz(x) (int)(x.size())
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define pb push_back
#define mp(a, b) make_pair(a, b)
#define fi first
#define se second
#define cmin(a, b) a = min(a, b)
#define cmax(a, b) a = max(a, b)
#define YES cout << "YES" << endl
#define NO cout << "NO" << endl
#define QYES quit("YES")
#define QNO quit("NO")
#define int long long
#define double long double
const int inf = numeric_limits<int>::max() / 4;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const int MOD = 1e9+7, LOG=20;
void solve();
signed main() {
ios::sync_with_stdio(0);
cin.tie(0);
int tt=1;
// cin >> tt;
while(tt--) solve();
return 0;
}
struct segtree {
int n;
vector<pair<int, int>> t, lazy;
segtree(int _n) : n(_n), t(4*n), lazy(4*n) {}
void push(int v, int l, int r) {
if (lazy[v]==mp(0LL, 0LL)) return;
t[v].fi+=lazy[v].fi;
t[v].se+=lazy[v].se;
if (l!=r) {
lazy[2*v+1].fi+=lazy[v].fi, lazy[2*v+1].se+=lazy[v].se;
lazy[2*v+2].fi+=lazy[v].fi, lazy[2*v+2].se+=lazy[v].se;
}
lazy[v]={0, 0};
}
void update(int v, int l, int r, int ql, int qr, pair<int, int> val) {
push(v, l, r);
if (l>qr || r<ql) return;
if (l>=ql && r<=qr) {
lazy[v]=val;
push(v, l, r);
return;
}
int m=(l+r)/2;
update(2*v+1, l, m, ql, qr, val);
update(2*v+2, m+1, r, ql, qr, val);
if ((t[2*v+1].fi==t[2*v+2].fi && t[2*v+1].se>t[2*v+2].se) || t[2*v+1].fi>t[2*v+2].fi) t[v]=t[2*v+1];
else t[v]=t[2*v+2];
}
pair<int, pair<int, int>> query(int v, int l, int r) {
push(v, l, r);
if (l==r) return {l, t[v]};
int m=(l+r)/2;
if (t[2*v+1].fi>t[2*v+2].fi || (t[2*v+1].fi==t[2*v+2].fi && t[2*v+1].se>t[2*v+2].se)) return query(2*v+1, l, m);
return query(2*v+2, m+1, r);
}
void update(int l, int r, pair<int, int> val) { update(0, 0, n-1, l, r, val); }
pair<int, pair<int, int>> query() { return query(0, 0, n-1); }
};
int n, k, m;
vector<int> a, p, in, out, is;
vector<vector<int>> adj;
set<int> ok, isin;
segtree seg(0);
int cnt=-1;
void dfs(int u, int val=0, int mn=0) {
if (u) {
cnt++;
in[u]=cnt, is[cnt]=u;
val+=a[u], cmin(mn, val);
seg.update(in[u], in[u], {mn, a[u]});
}
for (auto v: adj[u]) dfs(v, val, mn);
if (u) out[u]=cnt;
}
int find(int u) {
if (u==-1 || p[u]==u || ok.count(u)) return u;
return p[u]=find(p[u]);
}
void solve() {
read(n, k); n++;
seg=segtree(n-1);
int base=k;
adj.clear(), adj.resize(n), a.clear(), a.resize(n), p.clear(), p.resize(n);
in.clear(), in.resize(n), out.clear(), out.resize(n), is.clear(), is.resize(n);
for (int i=1; i<n; i++) {
read(a[i], p[i]);
adj[p[i]].pb(i);
}
for (int i=0; i<n; i++) ok.insert(i), isin.insert(i);
dfs(0);
auto q=seg.query();
while (k+q.se.fi>=0) {
int u=is[q.fi]; seg.update(in[u], in[u], {-inf, -inf}); isin.erase(u);
if (a[u]<0) {
q=seg.query();
continue;
}
ok.erase(u);
int par=find(p[u]);
if (par==0) {
seg.update(in[u], out[u], {-a[u], -a[u]});
k+=a[u];
a[u]=0;
q=seg.query();
continue;
}
if (!isin.count(par)) seg.update(in[par], in[par], {inf, inf}), isin.insert(par);
seg.update(in[par], out[par], {a[u], a[u]});
seg.update(in[u], out[u], {-a[u], -a[u]});
a[par]+=a[u];
a[u]=0;
q=seg.query();
}
cout << k-base << endl;
}
