CZ_PROB1  Summing to a Square Prime
$S_{P2} = \{p \mid p: \mathrm{prime} \wedge (\exists x_1, x_2 \in \mathbb{Z}, p = x_1^2 + x_2^2) \}$ is the set of all primes that can be represented as the sum of two squares. The function $S_{P2}(n)$ gives the $n$^{th} prime number from the set $S_{P2}$. Now, given two integers $n$ ($0 < n < 501$) and $k$ ($0 < k < 4$), find $p(S_{P2}(n), k)$ where $p(a, b)$ gives the number of unordered ways to sum to the given total ‘$a$’ with ‘$b$’ as its largest possible part. For example: $p(5, 2) = 3$ (i.e. $2+2+1$, $2+1+1+1$, and $1+1+1+1+1$). Here $5$ is the total with $2$ as its largest possible part.
Input
The first line gives the number of test cases $T$ followed by $T$ lines of integer pairs, $n$ and $k$.
Constraints
 $0 < T < 501$
 $0 < n < 501$
 $1 < S_{P2}(n) < 7994$
 $0 < k < 4$
Output
The $p(S_{P2}(n), k)$ for each $n$ and $k$. Append a newline character to every test cases’ answer.
Example
Input: 3 2 2 3 2 5 3 Output: 3 7 85
hide comments
untitledtitled:
20190116 23:58:12
There seems to be a problem with the rendering of the mathematical notation. The first line reads:


tanmayak99:
20180531 18:37:24
Good question..


deadpool_18:
20170619 18:39:42
do not forget to consider 2 in your set although its not congruent to 1 modulo 4 

harsh_verma:
20170615 14:05:19
due to small constraints can be solved without dp also ;) #PNC Last edit: 20170615 14:12:20 

shubham:
20170427 14:00:24
sometimes even the easy ones get you.. Wasted 1.5 hrs in this 

singhsauravsk:
20170410 04:31:08
Nice Problem :D


minhbk1861:
20161104 07:16:38
Wrong input constant


surayans tiwari(http://bit.ly/1EPzcpv):
20160626 14:51:52
coin change :) 

hash7:
20160624 18:47:46
Nyc qsn :) bottom up + precomputation 

:.Mohib.::
20150801 12:18:57
Nice One..!! 
Added by:  Rahul 
Date:  20070310 
Time limit:  0.714s 
Source limit:  3000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  Sam Collins 