{"code":"icpc21grouping","name":"Grouping","description":"There are $2n$ students in a school. Calculate the number of ways pick a group of at least 2 students so that for pair of\r\nstudents a and b in this group, $|a − b| \\ne 1$ and $|a − b| \\ne n + x$.\r\n\r\n

Input

\r\n\r\n- The first line of input contains 2 integers $n$ and $x (1 \\le n \\le 10^{18}, 0 \\le x \\le n)$.\r\n\r\n

Output

\r\n\r\n- Output a single integer, the answer to the problem modulo $10^9 + 7$.\r\n\r\n

Example

\r\n\r\n!!! question \"Test 1\"\r\n\r\n ???+ \"Input\"\r\n ```sample\r\n 2 1\r\n ```\r\n \r\n ???+ success \"Output\"\r\n ```sample\r\n 2\r\n ```\r\n \r\n ??? warning \"Note\"\r\n\r\n In the sample test case, we can pick {1, 3} or {2, 4}.","points":400.0,"partial":false,"time_limit":1.0,"memory_limit":262144,"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}}