ZSUM - Just Add It

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For two given integers n and k find (Zn + Zn-1 - 2Zn-2) mod 10000007, where Zn = Sn + Pn and Sn = 1k + 2k + 3k + … + nk and Pn = 11 + 22 + 33 + … + nn.

Input

There are several test cases (≤ 10000). In each case two space separated positive integers n and k are given.
For last test case n and k are given as 0 0, which is not to be processed.

Constraints

1 < n < 200000000
0 < k < 1000000

Output

For each case print the asked value in separate line.

Example

Input:
10 3
9 31
83 17
5 2
0 0

Output:
4835897
2118762
2285275
3694

hide comments
Gaurav Narula: 2016-02-29 12:19:43

Python TLE, Java TLE with fast io. Same logic with C AC :/

farhan764: 2016-01-31 16:15:55

modular exponentiation.......use wiki and math world

lakshay_v06: 2016-01-25 12:22:42

After simplifying the equation, you will have to use Modular exponentiation... :) -> MY 88th.

Last edit: 2016-01-25 12:24:26
darkhire21: 2015-12-24 06:44:52

In first go ...!!!

Vipul Srivastava: 2015-12-08 09:54:39

Same code gives TLE in Python

dragonemperor: 2015-10-21 07:52:48

AC at first go. Needed some time to reduce the equation though :)

MishThi: 2015-10-01 07:15:36

Python :( TLE

Last edit: 2015-10-01 07:15:49
Ravi Chandra: 2015-09-15 07:29:01

Hey my 54th

pvsmpraveen: 2015-08-29 07:46:30

Got AC, You will definitely learn something from this problem, I spent around 1.5 hour and its worth for it ;)

Last edit: 2015-08-29 07:47:01
prakash_reddy: 2015-08-26 20:39:36

simple question the task is to use effective algo for power of 2 numbers.. :)


Added by:Manohar Singh
Date:2011-09-04
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:Manohar Singh