#include<deque>
#include<queue>
#include<vector>
#include<algorithm>
#include<iostream>
#include<set>
#include<cmath>
#include<tuple>
#include<string>
#include<chrono>
#include<functional>
#include<iterator>
#include<random>
#include<unordered_set>
#include<array>
#include<map>
#include<iomanip>
#include<assert.h>
#include<list>
#include<bitset>
#include<stack>
#include<memory>
#include<numeric>
using namespace std;
using namespace std::chrono;
typedef long long int llint;
typedef long double lldo;
#define mp make_pair
#define mt make_tuple
#define pub push_back
#define puf push_front
#define pob pop_back
#define pof pop_front
#define fir first
#define sec second
#define res resize
#define ins insert
#define era erase
/*cout<<fixed<<setprecision(20);cin.tie(0);ios::sync_with_stdio(false);*/
const int mod=998244353 ;
const llint big=2.19e15+1;
const long double pai=3.141592653589793238462643383279502884197;
const long double eps=1e-4;
template <class T,class U>bool mineq(T& a,U b){if(a>b){a=b;return true;}return false;}
template <class T,class U>bool maxeq(T& a,U b){if(a<b){a=b;return true;}return false;}
llint gcd(llint a,llint b){if(a%b==0){return b;}else return gcd(b,a%b);}
llint lcm(llint a,llint b){if(a==0){return b;}return a/gcd(a,b)*b;}
template<class T> void SO(T& ve){sort(ve.begin(),ve.end());}
template<class T> void REV(T& ve){reverse(ve.begin(),ve.end());}
template<class T>llint LBI(const vector<T>&ar,T in){return lower_bound(ar.begin(),ar.end(),in)-ar.begin();}
template<class T>llint UBI(const vector<T>&ar,T in){return upper_bound(ar.begin(),ar.end(),in)-ar.begin();}

bool solve(void){
	int i,n,j,T;cin>>n>>T;
	if(n==0){return false;}
	static bool call[1001][1001];
	vector<int>M(n),L(n),K(n);
	for(i=0;i<n;i++){cin>>M[i]>>L[i]>>K[i];}
	for(i=0;i<n;i++){
		for(j=0;j<T;j++){call[j][i]=((j%(L[i]+K[i]))<=L[i]);}
	}
	
	int bmin=0,bmax=n;
	while(bmax-bmin>1){
		int bgen=(bmin+bmax)/2;
		int ope=bgen;
		vector<int>owa(T+1);
		vector<bool>finC(n);
		bool can=true;
		for(i=0;i<T;i++){
			ope+=owa[i];
			for(j=0;j<n;j++){
				if(finC[j]||ope==0||(!call[i][j])){continue;}
				if(i+M[j]>T){can=false;break;}
				ope--;
				owa[i+M[j]]++;
				finC[j]=1;
			}
			
		}
		for(j=0;j<n;j++){
			if(!finC[j]){can=false;break;}
		}
		if(can){bmax=bgen;}
		else{bmin=bgen;}
	}
	for(int bgen=bmax-1;bgen>=1&&bmax-bgen<100;bgen-=5){
		int ope=bgen;
		vector<int>owa(T+1);
		vector<bool>finC(n);
		bool can=true;
		for(i=0;i<T;i++){
			ope+=owa[i];
			for(j=0;j<n;j++){
				if(finC[j]||ope==0||(!call[i][j])){continue;}
				if(i+M[j]>T){can=false;break;}
				ope--;
				//cerr<<"i,j"<<i<<' '<<j<<endl;
				owa[i+M[j]]++;
				finC[j]=1;
			}
			
		}
		for(j=0;j<n;j++){
			if(!finC[j]){can=false;break;}
		}
		if(can){bmax=bgen;}
		
	}
	for(int bgen=bmax-1;bgen>=1&&bmax-bgen<100;bgen--){
		int ope=bgen;
		vector<int>owa(T+1);
		vector<bool>finC(n);
		bool can=true;
		for(i=0;i<T;i++){
			ope+=owa[i];
			for(j=0;j<n;j++){
				if(finC[j]||ope==0||(!call[i][j])){continue;}
				if(i+M[j]>T){can=false;break;}
				ope--;
				//cerr<<"i,j"<<i<<' '<<j<<endl;
				owa[i+M[j]]++;
				finC[j]=1;
			}
			
		}
		for(j=0;j<n;j++){
			if(!finC[j]){can=false;break;}
		}
		if(can){bmax=bgen;}
		
	}
	cout<<bmax<<endl;
	return true;
}
int main(void){
	cout<<fixed<<setprecision(20);cin.tie(0);ios::sync_with_stdio(false);
	while(solve()){}
	return 0;
}



Measured memory_bytes: 4092