Swarm of Polygons

Problem code: SWARM

All submissions for this problem are available.

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.

Input

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.

Constraints

1 <= t <= 30
3 <= n <= 109
3 <= k <= 20
1 <= b, c, m <= 106
0 <= a < m

Output

For each test case output the number of k-gons that can be formed modulo 1000000007.

Example

Input:
2
4 3 1 2 2 191
10 5 1 113 157 999991

Output:
1228
328836201

Author: spooky
Date Added: 13-04-2010
Time Limit: 10 sec
Source Limit: 50000 Bytes
Languages: ADA, ASM, BASH, BF, C, C99 strict, CAML, CLOJ, CLPS, CPP 4.0.0-8, CPP 4.3.2, CS2, D, ERL, F#, FORT, GO, HASK, ICK, ICON, JAR, JAVA, JS, LISP clisp, LISP sbcl, LUA, NEM, NICE, PAS fpc, PAS gpc, PERL, PERL6, PHP, PIKE, PRLG, PYTH, PYTH 3.1.2, RUBY, SCALA, SCM guile, SCM qobi, ST, TEXT, WSPC


Comments

Something is wrong with

pdwd @ 13 Aug 2010 01:11 AM

Something is wrong with submitting solution, it says wrong login or password when I try to submit my code.

my program runs fine in all

askishore999 @ 24 May 2011 12:15 PM
my program runs fine in all proper test cases still it doesnt get accepted???

my program is also running

haseeb448 @ 19 Jun 2011 06:48 PM
my program is also running for all test cases and according to me it is also very efficient but it doesn't get accepted... can i get somehow reason of failure??

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