{"code":"aicprtspk","name":"An interesting counting problem related to square product K","description":"Given $n, k (1 \\leq k \\leq n \\leq 10^6)$, count the number of arrays $a[]$ of size $k$ satisfies:\r\n\r\n- $1 \\leq a_1 < a_2 < \\dots < a_k \\leq n$.\r\n- $a_i \\times a_j$ is a perfect square $\\forall 1 \\leq i < j \\leq k$.\r\n\r\nSince the result can be large, output it under modulo $10^9 + 7$.\r\n\r\n<h4>Example</h4>\r\n\r\n!!! question \"Test 1\"\r\n\r\n    ???+ \"Input\"\r\n\r\n        ```sample\r\n        2 1\r\n        ```\r\n\r\n    ???+ success \"Output\"\r\n\r\n        ```sample\r\n        2\r\n        ```\r\n    \r\n    ??? warning \"Note\"\r\n        There are $2$ satisfied array of size $1$: {$1$}, {$2$}.\r\n\r\n!!! question \"Test 2\"\r\n\r\n    ???+ \"Input\"\r\n\r\n        ```sample\r\n        10 2\r\n        ```\r\n\r\n    ???+ success \"Output\"\r\n\r\n        ```sample\r\n        4\r\n        ```\r\n    \r\n    ??? warning \"Note\"\r\n        There are $4$ satisfied array of size $2$: {$1, 4$}, {$1, 9$}, {$2, 8$}, {$4, 9$}.\r\n\r\n!!! question \"Test 3\"\r\n\r\n    ???+ \"Input\"\r\n\r\n        ```sample\r\n        27 3\r\n        ```\r\n\r\n    ???+ success \"Output\"\r\n\r\n        ```sample\r\n        12\r\n        ```\r\n    \r\n    ??? warning \"Note\"\r\n        There are $12$ satisfied array of size $3$: {$1, 4, 9$}, {$1, 4, 16$}, {$1, 4, 25$}, {$1, 9, 16$}, {$1, 9, 25$}, {$1, 16, 25$}, {$2, 8, 18$}, {$3, 12, 27$}, {$4, 9, 16$}, {$4, 9, 25$}, {$4, 16, 25$}, {$9, 16, 25$}.","points":400.0,"partial":true,"time_limit":1.0,"memory_limit":1048576,"short_circuit":false,"allowed_languages":[3,4,34,36,37,5,6,11,12,14,28,2,38,39,9,18,17,29,23,27,35,25,26,10,7,19,32,1,8,15,16,24,20,33,13,41,21,40],"is_public":true,"is_manually_managed":false,"permissions":{"can_edit":false}}