ikshu-and-his-class-1
Problem Description
Ikshu and his class
Ikshu's class is very fond of playing games. Their teacher tied them with many ropes with each other, Such that each student is tied with exactly one rope. It means that if students 2 and 3 are connected and 2 is connected to 4 as well then 2,3 and 4 must be sharing the same rope.
Now, teacher asks them to divide themselves in group. One group for each rope, each group consists of the students tied to that particular rope. Each group exchanges gifts among themselves (each student is having exactly one gift before and after the game).
What is the total number of distinct exchanges possible ? Two exchanges are distinct if there is atleast one student having different gift with him.
NOTE: It is also possible that a student has same gift after exchanging as he had before exchanging. There might be a case where no exchange took place i.e each student is having same gift after exchanging as he was having before exchange.
Input: First line of input contains two integers N and K, where N is the number of students and K is the number of connections between students. Next K lines contains two integers which are the indices(0 based) of students connected by a rope.
Output: Print a single integer which is the total number of exchanges possible modulus (10^9 + 7)
Constraints: 1 ≤ N ≤ 100000 1 ≤ K ≤ 100000
SAMPLE INPUT 5 2 1 2 3 4
SAMPLE OUTPUT 4
Explanation
0 is alone, [1,2] and [3,4] are tied to same rope. Now, 0 cannot share gift with anyone whereas [1,2] can has two possible distinct exchanges a) where 1 and 2 exchange gifts b) where they do not exchange gift. Same for [3,4]
So, there are 2*2 = 4 different states possible at the end.
Contest Information
- Contest ID: 0
- Problem Index:
- Points: 0.0
- Rating: 0
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- Time Limit: None seconds
- Memory Limit: 0 bytes
Task
Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases.