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: Runtime Error)

#include <bits/stdc++.h>

using namespace std;

#define countof(a) (sizeof(a)/sizeof(*a))

#define vi vector<int>
#define vvi vector<vector<int> >
#define vpi vector<pi >
#define pi pair<int,int>
#define mp make_pair
#define fi first
#define se second
#define all(n) n.begin(), n.end()

#define FROMTO(var, from, to) for (register int var = (from), var##down = ((int)(to)) < ((int)(from));var##down ? (var >= (int)(to)) : (var <= (int)(to));var##down ? var-- : var++)
#define UPTO(var, from, to)   for (register int var = (from); var <= ((int)to); var++)
#define DOWNTO(var, from, to) for (register int var = (from); var >= ((int)to); var--)
#define FOR(var, to)          UPTO(var, 0, (to)-1)
#define DOWN(var, from)       DOWNTO(var, (from)-1, 0) 

#define INIT(var, val) FOR(i,countof(var)) var[i] = val
#define INPUT(var) FOR(i,countof(var)) cin >> var[i]
#define INPUT1(var) FOR(i,countof(var)) cin >> var[i], var[i]--

#define SORT(v) qsort(v,countof(v),sizeof(*v),int_less)
#define SORTT(v) qsort(v,countof(v),sizeof(*v),int_greater)
#define QSORT(v,b) qsort(v,countof(v),sizeof(*v),b)

#define MOD 1000000007
#define INF ((1 << 30)-1)
#define LINF ((1LL << 62)-1)

typedef uint8_t u8;
typedef uint16_t u16;
typedef uint32_t u32;
typedef uint64_t u64;
typedef int8_t s8;
typedef int16_t s16;
typedef int32_t s32;
typedef int64_t s64;

struct Comb {
    vector<vector<s64> > data;
    Comb(int n) { // O(n^2)
        data = vector<vector<s64> >(n+1,vector<s64>(n+1,1));
        UPTO(i,1,n) {
            FOR(j,i+1) {
                if (!j || j == i) data[i][j] = 1;
                else data[i][j] = data[i-1][j-1] + data[i-1][j];
            }
        }
    }
    
    s64 ncr(int n, int r) {
        return data[n][r];
    }
};

static inline int ri() {
  int a;
  scanf("%d", &a);
  return a;
}

int int_less(const void *a, const void *b) {
  return (*((const int*)a) - *((const int*)b));
}
int int_greater(const void *a, const void *b) {
  return (*((const int*)b) - *((const int*)a));
}

struct Graph {
	int n;
	vector<vector<pair<int, s64> > > hen;
	
	// result of Warshall–Floyd
	vector<vector<s64> > WF;
	bool wf_complete = false;
	
	// result of dijkstra
	vector<vector<s64> > DIJ;
	set<int> dij_completed;
	
	// result of Bellman–Ford
	vector<vector<s64> > BF;
	set<int> bf_completed;
	
	// result of dfs(reachable check)
	vector<vector<bool> > DFS;
	set<int> dfs_completed;
	
	Graph(int n) { // O(N)
		hen.resize(n, vector<pair<int, s64> >());
		DIJ.resize(n, vector<s64>());
		BF.resize(n, vector<s64>());
		DFS.resize(n, vector<bool>());
		this->n = n;
	}
	
	// return the position of negative cycle(-1 if none)
	int bf(int k) {
		bf_completed.insert(k);
		BF[k].resize(n,LINF);
		BF[k][k] = 0;
		FOR(i,n-1) {
			bool updated = false;
			FOR(j,n) {
				for (auto l : hen[j]) {
					if (BF[k][j] != LINF && BF[k][l.fi] > BF[k][j] + l.se)
						BF[k][l.fi] = BF[k][j] + l.se, updated = true;
				}
			}
			if (!updated) break;
		}
		
		FOR(j,n) {
			for (auto l : hen[j]) {
				if (BF[k][j] != LINF && BF[k][l.fi] > BF[k][j] + l.se) {
					return j; // negative loop
				}
			}
		}
		return -1;
	}
	int spfa(int k) {
		vector<bool> inque(n,false);
		vector<int> updated(n,0);
		
		bf_completed.insert(k);
		BF[k].resize(n,LINF);
		BF[k][k] = 0;
		
		queue<int> que;
		inque[k] = true;
		que.push(k);
		updated[k]++;
		while (que.size()) {
			int i = que.front(); que.pop();
			for (auto j : hen[i]) {
				if (BF[k][j.fi] > BF[k][i] + j.se) {
					BF[k][j.fi] = BF[k][i] + j.se;
					updated[j.fi]++;
					if (updated[j.fi] > n) return j.fi;
					if (!inque[j.fi]) {
						inque[j.fi] = true;
						que.push(j.fi);
					}
				}
			}
			inque[i] = false;
		}
		return -1;
	}
	
	int dij(int k) { // O(n+mlogm)
		assert(dij_completed.count(k) == 0);
		vector<int> updated(n,0);
		DIJ[k].resize(n,LINF);
		DIJ[k][k] = 0;
		priority_queue<pair<s64, int>, vector<pair<s64, int> >, greater<pair<s64,int> > > que;
		que.push(pair<s64,int>(0,k));
		while(que.size()) {
			auto i = que.top(); que.pop();
			for (auto j : hen[i.se]) {
				if (DIJ[k][j.fi] > i.fi + j.se) {
					DIJ[k][j.fi] = i.fi + j.se;
					que.push(pair<s64,int>(DIJ[k][j.fi], j.fi));
					updated[j.fi]++;
					if (updated[j.fi] >= n) return j.fi;
				}
			}
		}
		dij_completed.insert(k);
		return -1;
	}
	
	void wf() { // O(n^3)
		WF.resize(n, vector<s64>(n,LINF));
		FOR(i,n) {
			WF[i][i] = 0;
			for (auto j : hen[i]) {
				WF[i][j.fi] = j.se;
			}
		}
		FOR(k,n) {
			FOR(i,n) {
				FOR(j,n) {
					if (WF[i][k] != LINF && WF[k][j] != LINF) {
						WF[i][j] = min(WF[i][j], WF[i][k] + WF[k][j]);
					}
				}
			}
		}
		wf_complete = true;
	}
	
	void dfs(int from) {
		DFS[from].resize(n, false);
		DFS[from][from] = true;
		queue<int> que; que.push(from);
		while(que.size()) {
			auto i = que.front(); que.pop();
			for (auto j : hen[i]) {
				if (!DFS[from][j.fi]) {
					DFS[from][j.fi] = true;
					que.push(j.fi);
				}
			}
		}
		dfs_completed.insert(from);
	}
	
	bool reachable(int from, int to) {
		assert(dfs_completed.count(from));
		return DFS[from][to];
	}
	
	pair<bool,s64> shortest(int from, int to) {
		assert(wf_complete || dij_completed.count(from) || bf_completed.count(from));
		if (wf_complete)
			return mp(WF[from][to] != LINF, WF[from][to]);
		else if (dij_completed.count(from))
			return mp(DIJ[from][to] != LINF, DIJ[from][to]);
		else if (bf_completed.count(from))
			return mp(BF[from][to] != LINF, BF[from][to]);
		else return {}; // should not reached
	}
	
	void add_hen(int from, int to, s64 cost, bool muki) {
		hen[from].push_back(mp(to, cost));
		if (!muki) hen[to].push_back(mp(from, cost));
	}
};
// Graph.dfs : O(N)
// Graph.dij : O(N+MlogM)
// Graph.bf  : O(NM)
// Graph.wf  : O(N^3)
// Graph.reachable
// Graph.shortest

int main() {
    int n = ri();
	int m = ri();
	Graph graph(n);
	FOR(i,m) {
		int a = ri()-1;
		int b = ri()-1;
		graph.add_hen(a,b,-ri(),true);
	}
	
	int inf = graph.dij(0);
	if (inf != -1) {
		graph.dfs(inf);
		if (!graph.reachable(inf, n-1)) inf = -1;
	}
	
	if (inf == -1)
		cout << -graph.shortest(0,n-1).se << endl;
	else cout << "inf" << endl;
	
    return 0;
}