ASCDFIB - Ascending Fibonacci Numbers


John is trying to learn the Fibonacci sequence. This is what he has learned so far. The first two terms of the sequence are f(1) = 0 and f(2) = 1.  The next term f(n) is then calculated by adding the previous two terms f(n-1) and f(n-2). Therefore,

f(1) = 0

f(2) = 1

f(3) = f(2) + f(1) = 1 + 0 = 1

f(4) = f(3) + f(2) = 1 + 1 = 2

f(5) = f(4) + f(3) = 2 + 1 = 3

f(6) = f(5) + f(4) = 3 + 2 = 5

After calculating this for a while, John realized that the values are becoming too big. In order to keep the values small, John changed his algorithm. Instead of calculating f(n) = f(n-1)+f(n-2), he decided he will calculate f(n) = ( f(n-1)+f(n-2) ) % 10^5.

Now John wants to do some research on his new modified Fibonacci sequence. He will give you an integer A (A<=10^5) and an integer B (B<=10^6). You have to output all the terms from f(A) to f(A+B) in ascending order (non-decreasing order). But printing so many numbers is too much of a hassle. So, if there are more than 100 terms in the output, then only print the first 100.

Input

The first line contains an integer T (T<=100), which is the number of test cases.
Each test case contains two positive integers A and B as mentioned before.

Output

For each test case, print case number (Check sample output) and then print the terms from f(A)  to f(A+B) in ascending order (non-decreasing order). If there are more than 100 terms in the output, then only print the first 100.

Example

Input:

3 1 3 3 3 100 1 Output:

Case 1: 0 1 1 2 Case 2: 1 2 3 5 Case 3: 15075 69026

 


hide comments
vidusheeamoli: 2018-05-31 18:34:55

Counting sort :)

karthik_vg: 2018-03-10 17:08:59

matrix expo did the thing nice one (y)

code_aim: 2017-10-20 20:19:27

One of the worst problem statement. It should be made more clearer.

pruthi_vishal: 2017-01-29 10:25:27

Finally AC after 2WAs ...... Read the problem carefully before proceeding.......!!!!!!!

coder_hsnake: 2017-01-22 21:09:00

After 6 REs,1CE,1WA,3TLEs finally AC plz take array size for fibonacci 1100000 and use hashing not sorting :-)

nightwolf_9197: 2016-05-23 00:12:08

@forthright48: why is my code getting RE : SIGXFSZ error

darkhire21: 2016-01-02 19:51:20

after 1 month moved from todo to AC...!!!

eightnoteight: 2015-09-05 08:08:13

enjoyed solving it in python

Glenda Emanuella Sutanto: 2015-06-19 06:25:06

finally AC after 2 WAs and 1 TLE!!! :))) i just changed it into counting sort and it got AC xD

Glenda Emanuella Sutanto: 2015-06-18 06:35:17

@samiul / the problem setter : my submission 14478814 please check it, thankyou so much


Added by:forthright48
Date:2013-09-13
Time limit:3s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:Editorial