{"raw_statement":[{"iden":"problem statement","content":"Let us define the _beauty_ of a sequence $(a_1,... ,a_n)$ as the number of pairs of two adjacent elements in it whose absolute differences are $d$. For example, when $d=1$, the beauty of the sequence $(3, 2, 3, 10, 9)$ is $3$.\nThere are a total of $n^m$ sequences of length $m$ where each element is an integer between $1$ and $n$ (inclusive). Find the beauty of each of these $n^m$ sequences, and print the average of those values."},{"iden":"constraints","content":"*   $0 \\leq d < n \\leq 10^9$\n*   $2 \\leq m \\leq 10^9$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$n$ $m$ $d$"},{"iden":"sample input 1","content":"2 3 1"},{"iden":"sample output 1","content":"1.0000000000\n\nThe beauty of $(1,1,1)$ is $0$.  \nThe beauty of $(1,1,2)$ is $1$.  \nThe beauty of $(1,2,1)$ is $2$.  \nThe beauty of $(1,2,2)$ is $1$.  \nThe beauty of $(2,1,1)$ is $1$.  \nThe beauty of $(2,1,2)$ is $2$.  \nThe beauty of $(2,2,1)$ is $1$.  \nThe beauty of $(2,2,2)$ is $0$.  \nThe answer is the average of these values: $(0+1+2+1+1+2+1+0)/8=1$."},{"iden":"sample input 2","content":"1000000000 180707 0"},{"iden":"sample output 2","content":"0.0001807060"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}