BLAMOEBA - Super Amoeba


Peter has an amoeba farm with pretty much unlimited amoebae. After years of research, Peter created a device to convert some amoebae to super amoebae. However, his device can only be used once. Every day, a super amoeba will split into M super amoebae (2 < M < 100000).

Now, Peter plan his amoeba selling business. Initially, Peter converts X amoebae to super amoebae (X > 1). Every day after the amoebae split, Peter will take Y super amoebae for sale (Y > 1). After N days, Peter want all of his amoebae to be completely sold out (1 < N < 100000). Since the energy needed to convert amoebae is quite massive, X must be as small as possible. Help peter plan his business!

Input

First line is T, number of test cases (T < 100000). Next T lines each contains M and N separated by space.

Output

For each case, output X and Y separated by space. Since X and Y can be very large, output them with modulo 1000000007.

Example

Input:
1
4 3 Output: 21 64

Explanation

Initially, Peter has 21 super amoebae.
After day 1, there are 4 x 21 - 64 = 20 super amoebae
After day 2, there are 4 x 20 - 64 = 16 super amoebae
After day 3, there are 4 x 16 - 64 = 0 super amoeba
All the super amoebae are sold out after the 3rd day just as planned.


hide comments
prabhakar_jha: 2016-09-05 10:20:30

thnx andy for your response
andy i am using mod 1000000007 and using long then how i am getting overflow can you please tell.
I am a beginner please help
@Andy

Last edit: 2016-09-05 10:23:17
Andy: 2016-09-05 10:05:18

overflow

prabhakar_jha: 2016-09-05 09:51:45

Andy can you please look up at my solution i don't know why am i getting WA even i have tried some of my custom test cases for the submission 17652458
@Andy
waiting for you reply

Last edit: 2016-09-05 09:56:14
Andy: 2016-09-05 06:05:53

updated the description

[Rampage] Blue.Mary: 2016-09-05 06:00:47

According to the explanation, the input numbers should be "M and N separated by space."


Added by:Andy
Date:2016-09-04
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 GOSU
Resource:BLPCS4