Problem:
Score : 400 points

Problem Statement

There is a directed graph with N vertices and M edges.
The i-th edge (1≤i≤M) points from vertex a_i to vertex b_i, and has a weight c_i.
We will play the following single-player game using this graph and a piece.

Initially, the piece is placed at vertex 1, and the score of the player is set to 0.
The player can move the piece as follows:

When the piece is placed at vertex a_i, move the piece along the i-th edge to vertex b_i. After this move, the score of the player is increased by c_i.

The player can end the game only when the piece is placed at vertex N.
The given graph guarantees that it is possible to traverse from vertex 1 to vertex N.

When the player acts optimally to maximize the score at the end of the game, what will the score be?
If it is possible to increase the score indefinitely, print inf.

Constraints

2≤N≤1000

1≤M≤min(N(N-1),2000)

1≤a_i,b_i≤N (1≤i≤M)

a_i≠b_i (1≤i≤M)

a_i≠a_j or b_i≠b_j (1≤i<j≤M)

-10^9≤c_i≤10^9 (1≤i≤M)

c_i is an integer.

In the given graph, there exists a path from vertex 1 to vertex N.

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1 c_1
a_2 b_2 c_2
:
a_M b_M c_M

Output

Print the maximum possible score at the end of the game, if it is finite. If it is possible to increase the score indefinitely, print inf.

Sample Input 1

3 3
1 2 4
2 3 3
1 3 5

Sample Output 1

7

There are two ways to move the piece to vertex N=3:

vertex 1 → vertex 2 → vertex 3 : score 4+3=7

vertex 1 → vertex 3 : score 5

Thus, the maximum possible score at the end of the game is 7.

Sample Input 2

2 2
1 2 1
2 1 1

Sample Output 2

inf

It is possible to increase the score indefinitely by alternating between vertex 1 and 2.

Sample Input 3

6 5
1 2 -1000000000
2 3 -1000000000
3 4 -1000000000
4 5 -1000000000
5 6 -1000000000

Sample Output 3

-5000000000

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#define _USE_MATH_DEFINES
#pragma region include
#include <iostream>
#include <iomanip>
#include <stdio.h>

#include <sstream>
#include <algorithm>
#include <iterator>
#include <cmath>
#include <complex>

#include <string>
#include <cstring>
#include <vector>
#include <bitset>

#include <queue>
#include <set>
#include <map>
#include <stack>
#include <list>

#include <ctime>
////
#include <random>//
#pragma endregion //#include
/////////

#pragma region typedef
typedef long long LL;
typedef long double LD;
typedef unsigned long long ULL;
#pragma endregion //typedef
////定数
const int INF = (int)1e9;
const LL MOD = (LL)1e9+7;
const LL LINF = (LL)4e18+20;
const LD PI = acos(-1.0);
const double EPS = 1e-9;
/////////
using namespace::std;
/////////
#pragma region Math
#pragma region
template<class T>
inline T gcd(T a, T b){return b ? gcd(b, a % b) : a;}
#pragma endregion // 最大公約数 gcd
#pragma region
template<class T>
inline T lcm(T a, T b){return a / gcd(a, b) * b;}
#pragma endregion // 最小公倍数 lcm
#pragma region
LL powMod(LL num,LL n,LL mod=(LL)MOD){//(num**n)%mod
	num %= mod;//
	if( n == 0 ){
		return (LL)1;
	}
	LL mul = num;
	LL ans = (LL)1;
	while(n){
		if( n&1 ){
			ans = (ans*mul)%mod;
		}
		mul = (mul*mul)%mod;
		n >>= 1;
	}
	return ans;
}
LL mod_inverse(LL num,LL mod=MOD){
	return powMod(num,MOD-2,MOD);
}
#pragma endregion //繰り返し二乗法 powMod
#pragma region
template<class T>
vector<T> getDivisor(T n){
	vector<T> v;
	for(int i=1;i*i<=n;++i){
		if( n%i == 0 ){
			v.push_back(i);
			if( i != n/i ){//平方数で重複して数えないように
				v.push_back(n/i);
			}
		}
	}
	sort(v.begin(), v.end());
	return v;
}
#pragma endregion //約数列挙 getDivisor(n):O(√n)
#pragma endregion //math
//Utility:便利な奴
#pragma region
template<class T>
void UNIQUE(vector<T>& vec){
	sort(vec.begin(),vec.end());
	vec.erase(unique(vec.begin(),vec.end()),vec.end() );
}
#pragma endregion // sort erase unique
////////////////////////////////
#pragma region 
long long  bitcount64(long long bits)
{
    bits = (bits & 0x5555555555555555) + (bits >> 1 & 0x5555555555555555);
    bits = (bits & 0x3333333333333333) + (bits >> 2 & 0x3333333333333333);
    bits = (bits & 0x0f0f0f0f0f0f0f0f) + (bits >> 4 & 0x0f0f0f0f0f0f0f0f);
    bits = (bits & 0x00ff00ff00ff00ff) + (bits >> 8 & 0x00ff00ff00ff00ff);
    bits = (bits & 0x0000ffff0000ffff) + (bits >>16 & 0x0000ffff0000ffff);
    return (bits & 0x00000000ffffffff) + (bits >>32 & 0x00000000ffffffff);
}
#pragma endregion //その他
////////////////////////////////
struct edge_base{int to;LL cost;};
edge_base make_edge_base(int to,LL cost){
	edge_base ret = {to,cost};
	return ret;
}
#pragma region GRL
#pragma region //グラフ
template<class T,class EDGE>
void dijkstra(int root,int V,vector<T>& dist,vector<int>& prev,
	vector< vector<EDGE> > G	){
	priority_queue<pair<T,int>,vector<pair<T,int> >,greater<pair<T,int> > > que;
	
	dist.assign(V,LINF);
	prev.assign(V,-1);

	dist[root] = 0;
	que.push(pair<T,int>(0,root));//距離、頂点番号

	while( !que.empty() ){
		pair<T,int> p = que.top();que.pop();
		int v = p.second;
		if( dist[v] < p.first ) continue;
		for(int i=0;i < (int)G[v].size();++i){
			EDGE e = G[v][i];
			if( dist[e.to] > dist[v] + e.cost ){
				dist[e.to] = dist[v] + e.cost;
				prev[e.to] = v;
				que.push(pair<T,int>(dist[e.to],e.to));
			}
		}
	}
}
//経路復元,dijkstraにprev入れた
//http://ronly.hatenablog.com/entry/2017/06/17/161641
vector<int> get_path(vector<int>& prev,int t){
	vector<int> path;
	while(t!=-1){
		path.push_back( t );
		t = prev[t];
	}
	reverse(path.begin(),path.end());
	return path;
}
#pragma endregion //ダイクストラ法:O(|E|log|V|)
#pragma region //グラフ
void warshall_floyd(vector<vector<LL> >& dist,int V,const LL inf=LINF){
	for(int k=0;k<V;++k){
		for(int i=0;i<V;++i){
			if( dist[i][k] >= inf ) continue;
			for(int j=0;j<V;++j){
				if( dist[k][j] >= inf )continue;
				dist[i][j] = min(dist[i][j],dist[i][k]+dist[k][j]);
			}
		}
	}
}
#pragma endregion //ワーシャルフロイド:O(|V|**3)
#pragma region
namespace FLOW{
//vector< vector<FLOW:edge> > G;

struct edge_flow : public edge_base{
	LL cap;//LD cap;//
	int rev;
};
edge_flow make_edge_flow(int to,LL cap,int rev,LL cost=1){
//edge_flow make_edge_flow(int to,LD cap,int rev,LL cost=1){
	edge_flow ret;
	
	ret.to = to;
	ret.cost = cost;
	ret.cap = cap;
	ret.rev = rev;
	return ret;
}

//*
class Graph{
public:
	int V;
	vector< vector<FLOW::edge_flow> > G;
	vector< LL > dist;
	vector< int > iter;
	vector< bool > used;
	void init(int v){
		V = v;
		G.resize(V);
	}
	void reset(){
		iter.assign(V,0);
		used.assign(V,false);
	}
	//directed graph
	void add_edge(int from,int to,LL cap){
		G[from].push_back( FLOW::make_edge_flow(to,cap,G[to].size()) );
		G[to].push_back( FLOW::make_edge_flow(from,0,G[from].size()-1) );
	}
	
private:
	//sから最短距離をBFSで計算する
	void bfs(int s){//許容量もチェックしている
		queue<int> que;
		dist = vector<LL>(V,-1);
		dist[s] = 0;
		que.push(s);
		while(!que.empty()){
			int v = que.front();que.pop();
			for(int i=0;i<(int)G[v].size();++i){
				edge_flow &e = G[v][i];
				if( e.cap > 0 && dist[e.to] < 0 ){
					dist[e.to] = dist[v] + 1;
					que.push(e.to);
				}
			}
		}
	}
private:
	//増加パスをDFSで探す
	LL dfs(int v,int t,LL f){
		if( v==t ) return f;
		for(int &i = iter[v];i<(int)G[v].size();++i){//?
			FLOW::edge_flow &e = G[v][i];
			if( e.cap>0 && dist[v] < dist[e.to]){
				LL d = this->dfs(e.to, t, min(f,e.cap) );
				if( d > 0){
					e.cap -= d;
					G[e.to][e.rev].cap += d;
					return d;
				}
			}
		}
		return 0;
	}
public:
	//sからtへの最大流量を求める
	LL max_flow(int s,int t){
		LL flow = 0;
		for(;;){
			this->bfs(s);
			if( dist[t] < 0 ) return flow;
			iter = vector<int>(V,0);
			LL f = this->dfs(s,t,LINF);
			do{
				flow += f;
				f = this->dfs(s,t,LINF);
			}while( f > 0 );
		}
	}
};
//*/
}
#pragma endregion //dinic :O(|E||V|^2)
#pragma region //グラフ
bool is_bipartite(int v,int c,vector< vector<int> >& G,vector<int>& Color){
	Color[v] = c;
	for(int i=0;i < (int)G[v].size();++i){//隣接グラフ
		if(Color[ G[v][i] ] == c ) return false;
		if(Color[ G[v][i] ] == 0 && 
			!is_bipartite(G[v][i],-c,G,Color)
			){
				return false;
		}
	}
	return true;
}
bool is_bipartite(int Root,vector< vector<int> >& Graph){
	int GraphSize = Graph.size();
	vector<int> Color(GraphSize,0);
	const int ColorNo = 1;
	return is_bipartite(Root,ColorNo,Graph,Color);
}
#pragma endregion //二部グラフチェック is_bipartite(root,GraphList)
#pragma region
namespace matching{
//https://beta.atcoder.jp/contests/soundhound2018/tasks/soundhound2018_c
int V;		//頂点数
vector< vector<int> > G;//グラフ
vector<int> match;//match[i]:頂点[i]がどことマッチされているか
vector<bool > used;//
void add_edge(int u,int v){
	G[u].push_back(v);
	G[v].push_back(u);
}
 
bool dfs(int v){
	/*
	https://mathtrain.jp/bipartitematching
	未マッチ辺・マッチ辺・未マッチ辺
	これを
	マッチ辺・未マッチ辺・マッチ辺
	に変えると
	1マッチが2マッチになる。
	未[済未]
	増加路を求めている。
	*/
	used[v] = true;//dfsのroot前に初期化される
	int size = G[v].size();
	for(int i=0;i<size;++i){
		int u = G[v][i];//
		int w = match[u];//
		if( w<0 || ((used[w]==false) && dfs(w)) ){
			/*
			マッチングされていない||
			使われてない&&
			*/
			match[v] = u;
			match[u] = v;
			return true;
		}
	}
	return false;
}
 
int bipartite_matching(){
	int res = 0;
	match = vector<int>(V,-1);//未マッチ状態に初期化
	for(int v=0;v<V;++v){
		if( match[v] < 0 ){
			used = vector<bool>(V,false);
			if( dfs(v) ){
				++res;
			}
		}
	}
	return res;
}
}
#pragma endregion //二部グラフの最大マッチング bipartite_matching()
#pragma endregion //
#pragma region 
vector< vector<LL> > NCK;//初期値:0
//http://sugarknri.hatenablog.com/entry/2016/07/16/165715
void makeinv(vector<LL>& inv,const LL P){
	int i;
	//const int varMAX = max(100000,(int)inv.size());
	const int varMAX = max(300010,(int)inv.size());
	
	inv = vector<LL>( varMAX+1,0);
	inv[1]=1;
	for(i=2;i<=varMAX;i++){
		inv[i] = (inv[P%i] * (P-P/i)%P ) % P;//OVF
		//inv[i] = powMod(i,P-2,P);
	}
}

LL nCk(LL N,LL k,LL mod = MOD){
	static vector<LL> inv;//modの逆元
	if( inv.size() == 0 ){
		makeinv(inv,mod);//modは素数を入れる
	}
	k = min(k,N-k);
	if( k < 0 || k > N){return 0;}
	if( k == 0 ){return 1;}
	if( k == 1 ){return N%mod;}
	LL ret = 1;
	for(int i=1;i<=k;++i){
		ret = (ret * ((N+1-i)%mod) )%mod;//ret*N:OVF
		ret = (ret * inv[i] )%mod;
	}
	return ret;
}
LL nCk_once(LL N,LL k,LL mod = MOD){//modは素数
	k = min(k,N-k);
	if( k < 0 || k > N ){return 0;}
	if( k == 0 ){return 1;}
	if( k == 1 ){return N%mod;}
	LL ret = 1;
	LL A=1;
	for(LL i=0;i<k;++i){
		A = (A * ((N-i)%mod) ) % mod;
	}
	LL B=1;
	for(LL i=2;i<=k;++i){
		B = (B * (i%mod) ) % mod;
	}
	ret = ( A * powMod(B,mod-2,mod) ) % mod;
	return ret;
}
#pragma endregion //組み合わせnCk(,10^5)
#pragma region
LL nCk_base(int N,int K,LL mod=MOD){
	if( K<0 || N < K ) return 0;//多く取り過ぎ
	K = min(K,N-K);
	if( K==0 ){return 1%mod;}
	if( K==1 ){return N%mod;}//%MOD;
	if( N<=10000 && NCK[N][K] ){
		return NCK[N][K];
	}
	//N個目を使わない:nCk(N-1,k)
	//N個目を使う	:nCk(N-1,k-1)
	LL ans = (nCk_base(N-1,K)+nCk_base(N-1,K-1) )%mod;//%MOD;
	if( N<=10000 ){
		NCK[N][K] = ans;
	}
	return ans;
}

#pragma endregion //組み合わせ メモ?

#pragma region DSL
class UnionFind{
public:
	int cNum;//要素数
	vector<int> parent;
	vector<int> count;
	vector< vector<int> > GList;
	UnionFind(int n){
		cNum = n;
		parent = vector<int>(n);
		count = vector<int>(n,1);
		GList.resize(n);
		for(int i=0;i<n;++i){
			parent[i] = i;
			GList[i].push_back(i);
		}
	}
	int find(int x){
		if( parent[x] == x ){return x;}
		return parent[x] = find( parent[x] );
	}
	bool same(int x,int y){return find(x) == find(y);}
	int Count(int x){return count[find(x)];}
	void add(int x,int y){//union
		x = find(x);
		y = find(y);
		if( x==y )return;
		parent[x] = y;
		
		count[y] += count[x];
		if( GList[y].size() < GList[x].size() ){
			swap(GList[x],GList[y]);
		}
		GList[y].insert( GList[y].end(),
			GList[x].begin(),GList[x].end() );
	}
};
#pragma endregion //UnionFind
#pragma region DSL
class BITree{//1-index
	int N;
	vector<LL> bit;
public:
	BITree(int n){
		N = n;
		bit = vector<LL>(N+1,0);//1-index
	}
	void add(int a,LL w){//aにwを足す
		if( a <= 0 || N < a) return;//a:[1,N]
		for(int i=a;i<=N;i += i & -i){
			bit[i] += w;
		}
	}
	LL sum(int a){//[1,a]の和,a:[1,N]
		/*
		1番目からa番目までの和、1-index
		*/
		LL ret = 0;
		if( a > N ) a = N;
		for(int i=a; i > 0; i -= i & -i){
			ret += bit[i];
		}
		return ret;
	}
};
#pragma endregion //BIndexTree
#pragma region
template <typename T>
class segment_base{
	int N;//要素数
	vector< T > dat1;
	T VAL_E;//初期値
	T VAL_NULL;//空の値
public:
	segment_base(){};
	segment_base(int n,T val_E ):N(n),VAL_E(val_E){
		dat1.resize(2*n);
		dat1.assign(2*n,val_E);//初期化
	}
	void init(int n,T val_E,T val_N){
		N = n;
		VAL_E = val_E;
		VAL_NULL = val_N;
		int size = 2;
		while(size<N){
			size<<1;
		}
		N = size;
		dat1.resize(2*N);
		dat1.assign(2*N,val_E);
	}
	T SELECT(T& L,T& R){//扱う演算子
		T ans;
		ans = min(L,R);//
		return ans;
	}

	//index番目の値をvalに変更,indexは"0-index"
	void update(int i,T& val){
		i += N-1;
		dat1[i] = val;
		while(i>0){
			i = (i-1)/2;
			dat1[i] = SELECT(dat1[i*2+1],dat1[i*2+2]);
		}
	}

	//区間[L,R)のSELECT
	/*
	調べている範囲[a,b),階数k,見る場所[L,R)
	*/
	T query(int a,int b,int k,int L,int R){
		if( R<=a || b<=L ){
			return VAL_E;//交差しない
		}
		if( a<=L && R<=b && dat1[k] != VAL_NULL ){
			return dat1[k];
		}

		T res = VAL_E;
		int mid = (L+R)/2;
		if( a < mid ) res = SELECT(res,query(a,b,k*2+1,L,mid) );
		if( mid < b ) res = SELECT(res,query(a,b,k*2+2,mid,R) );
		return res;
	}
	T query(int L,int R){
		return query(L,R,0,0,N);
	}
};
#pragma endregion //segment_tree

#pragma region 
//行列の積
namespace mymat{
	LL matMOD = MOD;//初期値10^9 + 7
};
template<class T>
vector< vector<T> > operator*( vector<vector<T> >& A,vector< vector<T> >& B){
	LL mod = mymat::matMOD;
	int R = A.size();
	int cen = A[0].size();
	int C = B[0].size();
	vector< vector<T> > ans(R,vector<T>(C,0) );
	for(int row=0;row<R;++row){
		for(int col=0;col<C;++col){
			for(int inner=0;inner< cen;++inner){
				/*ans[row][col] = (ans[row][col] + A[row][inner]*B[inner][col])%mod;
				//ans[row][col] = (ans[row][col] + A[row][inner]*B[inner][col]);
				ans[row][col] = (ans[row][col] + mod) % mod;
				//負になるときの処理
				*/
				ans[row][col] = (ans[row][col] + A[row][inner]*B[inner][col])%mod;
			}
		}
	}
	return ans;
}

template<class T>
vector< vector<T> > powMod(const vector< vector<T> >& mat,LL N,LL mod=MOD){
	mymat::matMOD = mod;
	int R = mat.size();
	int C = mat[0].size();
	//R==C
	vector< vector<T> > I(R,vector<T>(C,0));//単位元
	for(int i=0;i<R && i<C;++i){
		I[i][i] = 1;
	}
	if( N == 0 ){
		return I;
	}
	vector< vector<T> > mul(R,vector<T>(C)),ans(R,vector<T>(C));
	ans = I;
	mul = mat;
	while(N){
		if( N & 1 ){
			ans = ans*mul;
		}
		N >>= 1;
		mul = mul*mul;
	}
	return ans;
}
#pragma endregion //行列

#pragma region
namespace TIME{
unsigned long long get_cycle(){
	return __rdtsc();
}
unsigned long long start,limit;
void time_start(){
	start = get_cycle();
}
//あたいをーさぐらないとーだめー
void time_set(unsigned long long num){limit = num;}
bool check(){return (get_cycle() < start+limit);}
}
#pragma endregion //時間計測

#pragma region

namespace RAND{
unsigned long xor128(){ 
	static unsigned long x=123456789,y=362436069,z=521288629,w=88675123; 
	unsigned long t; 
	t=(x^(x<<11));x=y;y=z;z=w;
	return( w=(w^(w>>19))^(t^(t>>8)) ); 
}
LL getRAND(LL P){
	return ((xor128()%P)+P)%P;
}
}

#pragma endregion //乱数

#pragma region
#pragma endregion //

//////////////////
void f(int root,vector<vector<edge_base> >& gra,vector<bool>& use){
	queue<int> now,next;
	next.push( root );
	use[root] = true;
	while(next.size()){
		now.swap(next);
		next = queue<int>();
		while(now.size()){
			int v = now.front();
			now.pop();
			int size = gra[v].size();
			for(int i=0;i<size;++i){
				int to = gra[v][i].to;
				if( use[to] == true ){
					continue;
				}
				use[to] = true;
				next.push( to );
			}
		}
	}
}
void solve(){
	int N,M;
	cin>>N>>M;
	vector< vector<edge_base> > G(N),rG(N);
	for(int i=0;i<M;++i){
		int a,b,c;
		cin>>a>>b>>c;
		--a;--b;
		c = -c;
		G[a].push_back(make_edge_base(b,c) );
		rG[b].push_back(make_edge_base(a,c) );
	}
	
	queue<int> que;
	que.push(0);
	vector<bool> useL(N,false);
	f(0,G,useL);
	vector<bool> useR(N,false);
	f(N-1,rG,useR);
	vector<bool> use(N,false);
	for(int i=0;i<N;++i){
		use[i] = useL[i]&useR[i];
	}
	
	vector<vector<edge_base> > gra(N);
	int NN = 0;
	for(int v=0;v<N;++v){
		if( use[v] == false ){
			continue;
		}
		++NN;
		int size = G[v].size();
		for(int i=0;i<size;++i){
			int to = G[v][i].to;
			if( use[to] == false ){
				continue;
			}
			gra[v].push_back( G[v][i] );
		}
	}
	////////
	const int start = 0;
	vector<LL> dist(N,LINF);
	dist[start] = 0;
	vector<bool> visit(N,false);
	queue<int> q[2];
	q[0].push( start );
	int now,next;
	int pos;
	int count = 0;
	for(;count<=N;++count){
		now = count%2;
		next = (now+1)%2;
		use = vector<bool>(N,false);
		if( q[now].size() == 0 ){
			break;
		}
		while( q[now].size() ){
			pos = q[now].front();
			q[now].pop();
			int size = gra[pos].size();
			for(int i=0;i<size;++i){
				int to = gra[pos][i].to;
				LL cost = gra[pos][i].cost;
				if( dist[to] > dist[pos] + cost ){
					dist[to] = dist[pos] + cost;
					if( visit[to] == false ){
						visit[to] = true;
						q[next].push( to );
					}
				}
			}
		}
	}
	if( count > N ){
		cout << "inf" << endl;
	}else{
		cout << -dist[N-1] << endl;
	}
}
#pragma region main
signed main(void){
	std::cin.tie(0);
	std::ios::sync_with_stdio(false);
	std::cout << std::fixed;//小数を10進数表示
	cout << setprecision(16);//小数点以下の桁数を指定//coutとcerrで別	

	solve();
}
#pragma endregion //main()