WEIRDFN - Weird Function

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Let us define :
F[1] = 1
F[i] = (a*M[i] + b*i + c)%1000000007 for i > 1

where M[i] is the median of the array {F[1],F[2],..,F[i-1]}.
The median of an array is the middle element of that array when it is sorted. If there are an even number of elements in the array, we choose the first of the middle two elements to be the median.

Given a,b,c and n, calculate the sum F[1] + F[2] + .. + F[n].

Input


The first line contains T the number of test cases. Each of the next T lines contain 4 integers : a,b,c and n.


Output

Output T lines, one for each test case, containing the required sum.

Example

Sample Input :
2
1 0 0 3
3 1 2 6

Sample Output :
3
103


Constraints

1 <= T <= 100
0 <= a,b,c < 1000000007
1 <= n <= 200000


Added by:Varun Jalan
Date:2010-01-25
Time limit:1.116s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel Pentium G860 3GHz)
Languages:All except: NODEJS PERL 6 SCM chicken VB.net
Resource:own problem used for Codechef Snackdown Onsite

hide comments
Harpreet Singh: 2014-12-04 18:26:36

strict^strict timelimit

SANDIPAN MANDAL: 2014-10-03 20:03:03

Getting WA. Plz provide some corner test cases

Kunal Behl: 2014-09-13 15:53:45

y time limit exceed everytime?? can anybody help please..

Matija Martiniæ: 2014-06-04 21:24:16

TLE even after using stl heap c++... :(
what to do now..??

sam17121991: 2014-04-23 19:14:51

oh my gosh!

(Tjandra Satria Gunawan)(曾毅昆): 2014-02-02 23:17:12

Time limit is too strict!

SaSukE: 2013-05-17 12:42:45

why implementation using red black tree is giving TLE ?? :/....Insertion and every query takes O(logn) still getting TLE ?? What should be the complexity of the solutn ??

Last edit: 2013-05-17 12:56:55
J.A.R.V.I.S.: 2013-02-03 13:36:52

Nice one :) solvable with STLs.. Watch out for overflows...

conioh: 2013-01-27 12:20:48

nice question...

Nilendu Das: 2012-12-09 20:07:18

Good question.. You can take help from RRATING problem from codechef..Jst the partition is diff..