Kernel Scheduler

You are developing the scheduling module for a new operating system. The module takes $n$ tasks to execute and the dependencies between them, then puts them in an order for execution.

More formally, the tasks are numbered from 1 to $n$. You are given $m$ dependencies numbered from 1 to $m$. The $i$-th dependency is described by two numbers $a_i$ and $b_i$, meaning that task $a_i$ must be executed before task $b_i$.

Sometimes there are cyclical dependencies: task $t_1$ must run before $t_2$, $t_2$ before $t_3$, ..., $t_{k-1}$ before $t_k$, and $t_k$ before $t_1$. Cyclical dependencies break scheduling, so you must remove some of the given dependencies so that the remaining set has no cycles.

However, you still need to keep at least $m/2$ of the original dependencies to preserve some of the original information. Write a program that performs this task.

The first line contains $n$ and $m$ ($2 \le n \le 10^5$, $1 \le m \le 3 \cdot 10^5$). Each of the next $m$ lines contains two numbers $a_i$ and $b_i$ ($1 \le a_i, b_i \le n$, $a_i \ne b_i$), describing the corresponding dependency between tasks $a_i$ and $b_i$.

The first line should contain YES if the desired subset of dependencies exists, and NO otherwise. In the YES case, the second line contains the number $k$ of selected dependencies (note that $k$ must be at least $m/2$), and the third line contains the $k$ ids of the selected dependencies. The ids are numbered from 1 to $m$ in input order.