Ring road bus routes

A country built a ring road along its border. The ring road has $N$ bus stops, numbered $0$ to $N-1$ in clockwise order. Several bus routes run on this road. A route is written $[a, b]$. Its bus runs clockwise from stop $a$ to stop $b$, then counterclockwise from $b$ back to $a$. So the stops that route $[a, b]$ visits are all the stops you meet going clockwise from $a$ until you reach $b$. No route visits every stop of the ring road.

The ministry of transport cancels some routes to cut costs. A route is cancelled when another route contains it. Route $[a, b]$ is contained in route $[c, d]$ when every stop that $[a, b]$ visits is also a stop that $[c, d]$ visits.

For example, let $N = 10$ with five routes given in this order: $[0, 4]$, $[2, 6]$, $[5, 0]$, $[7, 9]$, $[9, 4]$.

In the picture route 1 is contained in route 5, and route 4 is contained in route 3. No route contains route 2, route 3, or route 5. The cancelled routes are 1 and 4.

Given the routes, write a program that prints every route that is not cancelled.

The first line contains the number of bus stops $N$ ($3 \le N \le 1{,}000{,}000{,}000$). The second line contains the number of bus routes $M$ ($2 \le M \le 500{,}000$). The routes are numbered $1$ to $M$. Each of the next $M$ lines contains two integers $a$ and $b$ describing route $[a, b]$, starting with route 1. Here $0 \le a, b \le N-1$ and $a \ne b$, and no route is given more than once. No route visits every stop of the ring road.

Print the numbers of the routes that no other route contains, in increasing order, on one line. Separate the numbers with a single space.