Swarm of Polygons
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There is a regular n-gon. Some points are marked on each of its sides. There are x1 point marked on the first side, x2 – on the second, …, xn – on the nth. The marked points do not coincide with the vertices of the n-gon. You can choose no more than one of the marked points from each side and form a convex non-degenerate polygon by connecting all those points with lines. Now your task is to find the number of different k-gons that can be formed that way.
The first line of input file contains positive integer t – the amount of test cases. Next t lines contain six integers each: n, k, a, b, c, m. Here n is the number of sides of the initial n-gon. The amount of marked points on the first side of this n-gon is x1 = a, the amount of the marked points on the following sides is xi = (b*xi-1 + c) mod m, for i > 1.
1 <= t <= 30
3 <= n <= 109
3 <= k <= 20
1 <= b, c, m <= 106
0 <= a < m
For each test case output the number of k-gons that can be formed modulo 1000000007.
Input: 2 4 3 1 2 2 191 10 5 1 113 157 999991 Output: 1228 328836201
|Tags||aug10, medium, spooky|
|Time Limit:||1.25919 sec|
|Source Limit:||50000 Bytes|
|Languages:||C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, kotlin, PERL6, TEXT, SCM chicken, PYP3, CLOJ, R, COB, FS|
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