CSES - Investigation
  • Time limit: 1.00 s
  • Memory limit: 512 MB
You are going to travel from Syrjälä to Lehmälä by plane. You would like to find answers to the following questions:
  • what is the minimum price of such a route?
  • how many minimum-price routes are there? (modulo $10^9+7)$
  • what is the minimum number of flights in a minimum-price route?
  • what is the maximum number of flights in a minimum-price route?
Input

The first input line contains two integers $n$ and $m$: the number of cities and the number of flights. The cities are numbered $1,2,\ldots,n$. City 1 is Syrjälä, and city $n$ is Lehmälä.

After this, there are $m$ lines describing the flights. Each line has three integers $a$, $b$, and $c$: there is a flight from city $a$ to city $b$ with price $c$. All flights are one-way flights.

You may assume that there is a route from Syrjälä to Lehmälä.

Output

Print four integers according to the problem statement.

Constraints
  • $1 \le n \le 10^5$
  • $1 \le m \le 2 \cdot 10^5$
  • $1 \le a,b \le n$
  • $1 \le c \le 10^9$
Example

Input:
4 5
1 4 5
1 2 4
2 4 5
1 3 2
3 4 3


Output:
5 2 1 2