{"problem":{"name":"Ordinary Beauty","description":{"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 ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"soundhound2018_summer_qual_c"},"statements":[{"statement_type":"Markdown","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.\n\n## Constraints\n\n*   $0 \\leq d < n \\leq 10^9$\n*   $2 \\leq m \\leq 10^9$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$n$ $m$ $d$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"soundhound2018_summer_qual_c","tags":[],"sample_group":[["2 3 1","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: $(0+1+2+1+1+2+1+0)/8=1$."],["1000000000 180707 0","0.0001807060"]],"created_at":"2026-03-03 11:01:14"}}