#include <bits/stdc++.h>
using namespace std;
/*⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠛⣿⠀⠀⠀⠀⣤⣿⢻⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡛⠀⣤⣿⣿⣤⣤⣿⣿⣤⢸⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀
⢠⣼⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⢸⣿⣿⡟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣿⣿⣿⣿⣤⣤⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋
*/
#define fi first
#define se second
#define pb push_back
#define ins insert
#define sz(a) (int)(a.size())
#define all(x) (x).begin(),(x).end()
#define rep(i, a, b) for(int i = a; i < (b); ++i)
typedef long long ll;
typedef pair<int,int> pii;
typedef vector<int> vi;
void print(){cout<<'\n';}
template<class h,class...t>
void print(const h&v,const t&...u){cout<<v<<' ',print(u...);}
#define ONLINE_JUDGE
#ifndef ONLINE_JUDGE
#include "debug.h"
#else
#define debug(...)
#endif
//const int mod = 1e9+7;
//const int mod = 998244353;
const int MAXN=3e5+5;
const ll inf=1e9,INF=1e18;
struct Tree {
typedef ll T;
static constexpr T unit = -INF;
T f(T a, T b) { return max(a, b); } // (any associative fn)
vector<T> s; int n;
Tree(int n = 0, T def = unit) : s(2*n, def), n(n) {}
void update(int pos, T val) {
for (s[pos += n] = val; pos /= 2;)
s[pos] = f(s[pos * 2], s[pos * 2 + 1]);
}
T query(int b, int e) { // query [b, e)
T ra = unit, rb = unit;
for (b += n, e += n; b < e; b /= 2, e /= 2) {
if (b % 2) ra = f(ra, s[b++]);
if (e % 2) rb = f(s[--e], rb);
}
return f(ra, rb);
}
};
int n,x[MAXN],p[MAXN]; ll s;
vi g[MAXN]; ll ans = 0; vi nodes;
array<ll,3> R[MAXN];
void dfs(int v) {
for(int i : g[v]) dfs(i);
nodes.pb(v);
}
void solve(int tc = 0){
cin>>n>>s;
rep(i,1,n+1) {
cin>>x[i]>>p[i];
g[p[i]].pb(i);
}
set<array<ll,3>> S;
rep(i,1,n+1) {
if(!p[i]) {
dfs(i); ll sum = 0; int N = sz(nodes);
Tree tr(N + 5); tr.update(0,0);
stack<pair<ll,int>> st; st.push({0,-1});
rep(j,0,N) {
sum += x[nodes[j]];
while(st.size() and sum - st.top().fi <= 0) st.pop();
if(st.empty()) R[nodes[j]] = {INF,0,0};
else {
int l = st.top().se; ll k = sum - tr.query(l+1,j+2);
R[nodes[j]] = {-k,l == -1 ? 0 : nodes[l],sum - st.top().fi};
}
st.push({sum,j});
tr.update(j+1,sum);
} S.ins(R[i]);
nodes.clear();
}
}
while(S.size()) {
auto [drop,nxt,add] = *(S.begin()); S.erase(S.begin());
if(s - drop < 0) break;
s += add; ans += add;
if(nxt != 0) S.ins(R[nxt]);
} print(ans);
}
signed main(){
ios_base::sync_with_stdio(false); cin.tie(0);
int tc=1;
//cin>>tc;
for(int t = 0; t < tc; t++) solve(t);
}
