K Perfect Matchings

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You are given a bipartite graph $G = (U, V , E)$, and an integer $K$. $U$ and $V$ are the two bipartitions of the graph such that $U$ = $V$ = $N$ , and $E$ is the edge set. The vertices of $U$ are {$1, 2, . . . , N$ } and that of $V$ are {$N + 1, N + 2, . . . , 2N$ }. You need to find out whether the total number of different perfect matchings in $G$ is strictly greater than $K$ or not. Recall that a perfect matching is a subset of $E$ such that every vertex of the graph belongs to exactly one edge in the subset. Two perfect matchings are considered to be different even if one edge is different. ###Input First line of the input contains three integers: $N$, $M$ and $K$, which represent $U$ (which is also equal to $V$), $E$ and the queried threshold respectively. The ith of the next $E$ lines contains two numbers $L_i$ and $R_i$ which denote the ith edge is between the vertices $L_i$ and $R_i$. ###Output A single line containing “Yes” if the number of perfect matchings is greater than $K$, and “No” othewise. ###Constraints  $1 \leq N \leq 100$  $1 \leq M \leq 600$  $0 \leq K \leq 10^5$  $1 \leq L_i \leq N \lt R_i \leq 2 * N$ ###Subtasks ###Subtask 1 (10 Points):  $K = 0$ ###Subtask 2 (30 Points):  $1 \leq N \leq 50$  $1 \leq M \leq 100$  $0 \leq K \leq 300$ ###Subtask 3 (60 Points):  No further constraints. ###Sample Input 1 3 5 2 1 4 2 6 2 5 3 5 3 6 ###Sample Output 1 No ###Sample Input 2 3 5 1 1 4 2 6 2 5 3 5 3 6 ###Sample Output 2 Yes ###Explanation: *Explanation 1:* The graph is as follows: There are exactly two perfect matchings in this graph: {(1, 4), (2, 5), (3, 6)} and {(1, 4), (2, 6), (3, 5)}. The number of perfect matchings is not $\gt K$, and hence the output is “No”. *Explanation 2:* The graph is the same as previous one, and the same 2 perfect matchings are present. But now, $K$ is 1. Therefore, the number of perfect matchings is > $K$, and hence the output is “Yes”.Author:  admin2 
Tags  admin2 
Date Added:  20062018 
Time Limit:  1 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, kotlin, PERL6, TEXT, SCM chicken, CLOJ, COB, FS 
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