#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
const ll mod = 1000000007;
const ll INF = (1e+18) + 7;
typedef pair<int, int>P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;
typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-12;
const ld pi = acos(-1.0);
//typedef vector<vector<ll>> mat;
typedef vector<int> vec;

ll mod_pow(ll a, ll n, ll m) {
	ll res = 1;
	while (n) {
		if (n & 1)res = res * a%m;
		a = a * a%m; n >>= 1;
	}
	return res;
}

struct modint {
	ll n;
	modint() :n(0) { ; }
	modint(ll m) :n(m) {
		if (n >= mod)n %= mod;
		else if (n < 0)n = (n%mod + mod) % mod;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
modint operator+=(modint &a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; }
modint operator-=(modint &a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; }
modint operator*=(modint &a, modint b) { a.n = ((ll)a.n*b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, int n) {
	if (n == 0)return modint(1);
	modint res = (a*a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p%a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }

const int max_n = 1 << 18;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}
using mP = pair<modint, modint>;

int dx[4] = { 0,1,0,-1 };
int dy[4] = { 1,0,-1,0 };

int take_first(bitset<1000> bt) {
	int c = bt.count();
	int res = 0;
	per(i, 10) {
		if ((bt >> (1 << i)).count() == c) {
			res += (1 << i);
			bt >>= (1 << i);
		}
	}
	return res;
}

int n, t;
void solve() {
	vector<vector<bool>> exi(n, vector<bool>(t + 1));
	vector<int> m(n);

	vector<bitset<1000>> loc(t + 1);
	rep(i, n) {
		cin >> m[i];
		int l, k; cin >> l >> k;
		int cur = 0;
		while (cur <= t) {
			Rep1(j, cur, cur + l) {
				if (j > t)break;
				exi[i][j] = true;
				loc[j][i] = 1;
			}
			cur += l + k;
		}
	}
	for (int x = 1; x <= n; x++) {
		bitset<1000> rest; rep(i, n)rest[i] = 1;
		vector<int> ad(t + 1, 0);
		int cur = x;
		rep(i, t + 1) {
			cur += ad[i];
			if (cur == 0)continue;
			bitset<1000> bt = rest & loc[i];
			int c = bt.count();
			bool fin = false;
			int len = min(c, cur);
			rep(j, len) {
				int f = bt._Find_first();
				//cout << "! " << x << " " << i << " " << f << endl;
				if (i + m[f] <= t) {
					rest[f] = 0;
					bt[f] = 0;
					cur--;
					ad[i + m[f]]++;
				}
				else {
					fin = true; break;
				}
			}
			if (fin)break;
		}
		bool valid = true;
		rep(i, n)if (rest[i])valid = false;
		if (valid) {
			//cout << "ans is ";
			cout << x << endl; return;
		}
	}
}


signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(10);
	//init_f();
	//init();
	//int t; cin >> t; rep(i, t)solve();
	while (cin >> n >> t, n) {
		solve();
	}
	//solve();
	//stop
	return 0;
}



Measured memory_bytes: 7540