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CSES Problem Set

Course Schedule II


Task | Statistics


CSES - Course Schedule IICSES - Course Schedule II

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
Example

Input:
4 2
2 1
2 3


Output:
2 1 3 4