CSES - Course Schedule
  • Time limit: 1.00 s
  • Memory limit: 512 MB
You have to complete $n$ courses. There are $m$ requirements of the form "course $a$ has to be completed before course $b$". Your task is to find an order in which you can complete the courses.

Input

The first input line has two integers $n$ and $m$: the number of courses and requirements. The courses are numbered $1,2,\dots,n$.

After this, there are $m$ lines describing the requirements. Each line has two integers $a$ and $b$: course $a$ has to be completed before course $b$.

Output

Print an order in which you can complete the courses. You can print any valid order that includes all the courses.

If there are no solutions, print "IMPOSSIBLE".

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

Input:
5 3
1 2
3 1
4 5


Output:
3 4 1 5 2