#include <bits/stdc++.h>
using namespace std;
#define ff endl
#define lf "\n"
#define fi first
#define se second
#define _ << ' ' <<
#define all(x) begin(x),end(x)
#define rall(x) rbegin(x),rend(x)
#ifdef DEBUG
constexpr bool IS_DEBUG = 1;
#define infor(fmt, ...) do { print(stderr, fmt, ##__VA_ARGS__); } while(0)
#define infof(fmt, ...) do { println(stderr, fmt, ##__VA_ARGS__); } while(0)
#else
constexpr bool IS_DEBUG = 0;
#define infor(fmt, ...)
#define infof(fmt, ...)
#endif
using ll = long long;
using pll = pair<ll, ll>;
using pii = pair<int, int>;
template<typename... Args>
using vec = vector<Args...>;
constexpr int LOG = 20;
constexpr int MOD = 1e9+7;
constexpr int MAXN = 1e5+7;
mt19937 timmy_loves_gambling(73);
constexpr ll INF = 2e18;
int main(void) {
ios::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
int N; cin >> N;
ll S; cin >> S;
vec<int> W(N + 1);
vec<vec<int>> adj(N + 1);
for(int i = 1; i <= N; ++i) {
int x, p; cin >> x >> p;
W[i] = x;
adj[p].emplace_back(i);
}
vec<ll> mn(N + 1, 0), p(N + 1, 0);
vec<priority_queue<pll, vec<pll>, greater<pll>>> q(N + 1);
auto dfs = [&](int v, auto &&dfs) -> void {
for(auto u: adj[v]) {
dfs(u, dfs);
if(mn[u] < INF) {
q[v].emplace(mn[u], u);
}
}
p[v] = W[v];
while(!q[v].empty() && p[v] <= 0) {
auto [m, u] = q[v].top();
q[v].pop();
mn[v] = max({mn[v], mn[u] - p[v], -p[v]});
p[v] += p[u];
if(q[v].size() < q[u].size()) {
swap(q[u], q[v]);
}
while(!q[u].empty()) {
q[v].emplace(q[u].top());
q[u].pop();
}
}
if(p[v] <= 0) {
mn[v] = INF;
}
};
dfs(0, dfs);
infof("mn: {}", mn);
infof(" p: {}", p);
ll profit = 0;
priority_queue<pll, vec<pll>, greater<pll>> r;
r.emplace(mn[0], 0);
while(!r.empty()) {
auto [m, v] = r.top();
r.pop();
if(S + profit < m) break;
profit += p[v];
if(r.size() < q[v].size()) {
swap(r, q[v]);
}
while(!q[v].empty()) {
r.emplace(q[v].top());
q[v].pop();
}
}
cout << profit << lf;
}
