{"raw_statement":[{"iden":"problem statement","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 $B_i > B_j$."},{"iden":"constraints","content":"*   All values in input are integers.\n*   $1 \\leq N \\leq 2000$\n*   $1 \\leq K \\leq 10^9$\n*   $1 \\leq A_i \\leq 2000$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $K$\n$A_0$ $A_1$ $...$ $A_{N - 1}$"},{"iden":"sample input 1","content":"2 2\n2 1"},{"iden":"sample output 1","content":"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 $3$."},{"iden":"sample input 2","content":"3 5\n1 1 1"},{"iden":"sample output 2","content":"0\n\n$A$ may contain multiple occurrences of the same number."},{"iden":"sample input 3","content":"10 998244353\n10 9 8 7 5 6 3 4 2 1"},{"iden":"sample output 3","content":"185297239\n\nBe sure to print the output modulo $10^9 + 7$."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}