#include <bits/stdc++.h>
using namespace std;

#define ll long long

const ll maxn = 4000;
const ll maxk = 12000;

ll n, k;
ll dp[2][maxk+1];
ll max_ado[2][maxk+1];
ll ar[maxn+1];
ll ertek[maxn+1];
ll ado[maxn+1];

void solve() {
    cin >> n >> k;
    for(ll i = 1; i <= n; ++i) cin >> ar[i] >> ertek[i] >> ado[i];
    dp[1][ar[1] + ado[1]] = ertek[1];
    max_ado[1][ar[1] + ado[1]] = ado[1];
    for(ll i = 1; i < n; ++i) {
        for(ll j = 0; j <= k; ++j) {
            if(dp[(i + 1) % 2][j] < dp[i % 2][j]) {
                dp[(i + 1) % 2][j] = dp[i % 2][j];
                max_ado[(i + 1) % 2][j] = max_ado[i % 2][j];
            }
            if(dp[(i + 1) % 2][j - max_ado[i % 2][j] + max(max_ado[i % 2][j], ado[i + 1]) + ar[i + 1]] < dp[i % 2][j] + ertek[i + 1]) {
                dp[(i + 1) % 2][j - max_ado[i % 2][j] + max(max_ado[i % 2][j], ado[i + 1]) + ar[i + 1]] = dp[i % 2][j] + ertek[i + 1];
                max_ado[(i + 1) % 2][j - max_ado[i % 2][j] + max(max_ado[i % 2][j], ado[i + 1]) + ar[i + 1]] = max(max_ado[i % 2][j], ado[i + 1]);
            }
        }
    }
    ll maxi = 0;
    for(ll i = 0; i <= k; ++i) maxi = max(maxi, dp[n % 2][i]);
    cout << maxi << "\n";
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    solve();
    return 0;
}