{"problem":{"name":"Kleene Inversion","description":{"content":"We have a sequence of $N$ integers $A~=~A_0,~A_1,~...,~A_{N - 1}$. Let $B$ be a sequence of $K \\times N$ integers obtained by concatenating $K$ copies of $A$. For example, if $A~=~1,~3,~2$ and $K~=~2$","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"jsc2019_qual_b"},"statements":[{"statement_type":"Markdown","content":"We have a sequence of $N$ integers $A~=~A_0,~A_1,~...,~A_{N - 1}$.\nLet $B$ be a sequence of $K \\times N$ integers obtained by concatenating $K$ copies of $A$. For example, if $A~=~1,~3,~2$ and $K~=~2$, $B~=~1,~3,~2,~1,~3,~2$.\nFind the inversion number of $B$, modulo $10^9 + 7$.\nHere the inversion number of $B$ is defined as the number of ordered pairs of integers $(i,~j)~(0 \\leq i < j \\leq K \\times N - 1)$ such that $B_i > B_j$.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\leq N \\leq 2000$\n*   $1 \\leq K \\leq 10^9$\n*   $1 \\leq A_i \\leq 2000$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $K$\n$A_0$ $A_1$ $...$ $A_{N - 1}$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"jsc2019_qual_b","tags":[],"sample_group":[["2 2\n2 1","3\n\nIn this case, $B~=~2,~1,~2,~1$. We have:\n\n*   $B_0 > B_1$\n*   $B_0 > B_3$\n*   $B_2 > B_3$\n\nThus, the inversion number of $B$ is $3$."],["3 5\n1 1 1","0\n\n$A$ may contain multiple occurrences of the same number."],["10 998244353\n10 9 8 7 5 6 3 4 2 1","185297239\n\nBe sure to print the output modulo $10^9 + 7$."]],"created_at":"2026-03-03 11:01:14"}}