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Micro and Challenge

Problem

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Micro just read an amazing article on Topological Sorting. He was so impressed by it, that he went to the Code shop, purchased a Directed Acyclic Graph, and started applying Topological Sort on it. He tried finding out total number of topological sorting possible, for its vertices. He successfully did that and called that number $$T$$. Now, he tried another challenge, but got stuck. The challenge is to find the $$K^{th}$$ lexicographically largest topological sorting of the vertices. Help Micro find this out.

**Input:**

First line consists of three space separated integers, $$N$$ - number of vertices, $$M$$ - number of edges and $$K$$ - as described in the question.

Each of the following $$M$$ lines contain two space separated integers $$X$$, and $$Y$$ denoting there is an from $$X$$ to $$Y$$.

**Output:**

Print $$N$$ space separated integers denoting the $$K^{th}$$ lexicographically largest topological sorting.

**Constraints:**

$$1 \le N \le 20$$

$$1 \le M \le 50$$

$$1 \le X, Y \le N$$

$$1 \le K \le T \le 10^{15}$$

Time Limit:
1.0 sec(s)
for each input file.

Memory Limit:
256 MB

Source Limit:
1024 KB

Marking Scheme:
Marks are awarded when all the testcases pass.

Allowed Languages:
C,
C++,
C++14,
Clojure,
C#,
D,
Erlang,
F#,
Go,
Groovy,
Haskell,
Java,
Java 8,
JavaScript(Rhino),
JavaScript(Node.js),
Julia,
Lisp,
Lisp (SBCL),
Lua,
Objective-C,
OCaml,
Octave,
Pascal,
Perl,
PHP,
Python,
Python 3,
R(RScript),
Racket,
Ruby,
Rust,
Scala,
Swift,
Visual Basic,
Kotlin

Initializing Code Editor...

{"578bb83": "/pagelets/recommended-problems/algorithm/micro-and-arrangement/", "578bb30": "/pagelets/problem-author-tester/algorithm/micro-and-arrangement/", "578bb52": "/pagelets/problems-hint/algorithm/micro-and-arrangement/", "578bb0e": "/pagelets/suggested-problems/algorithm/micro-and-arrangement/", "578bae1": "/pagelets/show-submission/algorithm/micro-and-arrangement/"}

{}

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