| Time limit: | 1.00 s |
Memory limit: | 512 MB |
You want to complete $n$ courses that have requirements of the form "course $a$ has to be completed before course $b$".
You want to complete course $1$ as soon as possible. If there are several ways to do this, you want then to complete course $2$ as soon as possible, and so on.
Your task is to determine the order in which you complete the courses.
Input
The first input line has two integers $n$ and $m$: the number of courses and requirements. The courses are numbered $1,2,\dots,n$.
Then, there are $m$ lines describing the requirements. Each line has two integers $a$ and $b$: course $a$ has to be completed before course $b$.
You can assume that there is at least one valid schedule.
Output
Print one line having $n$ integers: the order in which you complete the courses.
Constraints
- $1 \le n \le 10^5$
- $1 \le m \le 2 \cdot 10^5$
- $1 \le a,b \le n$
Example
Input:
4 2
2 1
2 3
Output:
2 1 3 4
