$S_{P2} = \{p \mid p: \mathrm{prime} \wedge (\exists x_1, x_2 \in \mathbb{Z}, p = x_1^2 + x_2^2) \}$ 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