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CSES Problem Set

# Critical Cities

CSES - Critical CitiesCSES - Critical Cities

 Time limit: 1.00 s Memory limit: 512 MB

There are $n$ cities and $m$ flight connections between them. A city is called a critical city if it appears on every route from a city to another city.

Your task is to find all critical cities from Syrjälä to Lehmälä.

Input

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

Then, there are $m$ lines describing the roads. Each line has two integers $a$ and $b$: there is a flight from city $a$ to city $b$. All flights are one-way flights.

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

Output

First print an integer $k$: the number of critical cities. After this, print $k$ integers: the critical cities in increasing order.

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

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

Output:
3 1 2 5