- 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
- 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 and : the number of cities and the number of flights. The cities are numbered . City 1 is Syrjälä, and city is Lehmälä.
After this, there are lines describing the flights. Each line has three integers , , and : there is a flight from city to city with price . 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
Example
Input:
4 5 1 4 5 1 2 4 2 4 5 1 3 2 3 4 3
Output:
5 2 1 2