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: Accepted)

#if !defined(__clang__) && defined(__GNUC__)
#include <bits/stdc++.h>
#else
#include <cstdlib>
#include <climits>
#include <iostream>
#include <cstdint>
#include <vector>
#include <string>
#include <complex>
#include <bitset>
#include <queue>
#include <deque>
#include <stack>
#include <utility>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <regex>
#endif //  !defined(__clang__) && defined(__GNUG__)
#include <boost/lexical_cast.hpp>
#include <boost/algorithm/string.hpp>
#include <boost/multi_array.hpp>

using namespace std;

#include <boost/optional.hpp>



/// 距離つきグラフ
template<typename T, typename D, D nonval>
class Gr {
public:
    using edge = std::unordered_map<T, D>;
    using vertex_iterator = typename std::unordered_map<T, edge>::iterator;
    using vertex_const_iterator = typename std::unordered_map<T, edge>::const_iterator;

    Gr(T vertex_count, T edge_count) :
        vertex_count_(vertex_count), edge_count_(edge_count)
    {}

    // 値設定
    void set(T from, T to, D distance) {
        mat_[from][to] = distance;
    }

    // 距離
    D distance(T from, T to) const {
        if (mat_.find(from) != mat_.end()) {
            if (mat_[from].find(to) != mat_[from].end()) {
                return mat_[from][to];
            }
        }
        return nonval;
    }

    // 起点頂点をイテレート
    vertex_iterator from_vertex_begin() {
        return mat_.begin();
    }
    vertex_iterator from_vertex_end() {
        return mat_.end();
    }

    vertex_const_iterator from_vertex_cbegin() const {
        return mat_.begin();
    }

    vertex_const_iterator from_vertex_cend() const {
        return mat_.end();
    }

    // とある起点頂点からの辺をイテレート
    typename edge::iterator edge_begin(T from) {
        return mat_[from].begin();
    }
    typename edge::iterator edge_end(T from) {
        return mat_[from].end();
    }

    /**
        最短経路を計算

        ベルマンフォード法 O(V*E)

        @code
        int64_t N, M;
        std::cin >> N >> M;

        Gr<int64_t, int64_t, 0> g(N, M);
        for (size_t i = 0; i < M; ++i) {
            int64_t a, b, c;
            std::cin >> a >> b >> c;
            a--;
            b--;
            g.set(a, b, c);
        }
        @endcode
    */
    boost::optional<std::vector<T>> find_shortest_path(T start, T loop_detect_goal) const {
        constexpr T INF = std::numeric_limits<T>::max() / 2 + 1;
        std::vector<D> d(vertex_count_, INF);
        d[start] = 0;

        for (T i = 0; i < vertex_count_ * 2; ++i) {
            bool update = false;
            // 辺をイテレート
            for (auto&& f = from_vertex_cbegin();
                 f != from_vertex_cend();
                 ++f)
            {
                for (auto&& e = f->second.begin();
                     e != f->second.end();
                     ++e)
                {
                    const auto from = f->first;
                    const auto to = e->first;
                    const auto cost = e->second;
                    if (d[from] != INF && d[to] > d[from] + cost) {
                        d[to] = d[from] + cost;
                        update = true;

                        if (i >= vertex_count_ - 1 && to == loop_detect_goal) {
                            return boost::none;
                        }

                    }
                }
            }
            if (!update) {
                break;
            }
         }
         return d;
    }

private:
    T vertex_count_;
    T edge_count_;
    std::unordered_map<T, edge> mat_;
};

int main()
{
    int64_t N, M;
    std::cin >> N >> M;

    Gr<int64_t, int64_t, 0> g(N, M);
    for (size_t i = 0; i < M; ++i) {
        int64_t a, b, c;
        std::cin >> a >> b >> c;
        a--;
        b--;
        g.set(a, b, c * -1LL);
    }

    auto d = g.find_shortest_path(0, N-1);
    if (!d) {
        std::cout << "inf" << std::endl;
    }
    else {
        int64_t r = (*d)[N-1] * (-1ll);
        std::cout << r << std::endl;
    }

    return 0;
}