Sum of Distinct Primes

Every positive integer can be written as a sum of distinct primes. Given two integers $n$ and $k$, write a program that counts the number of ways to write $n$ as a sum of $k$ distinct primes. Two representations that differ only in the order of the summands (for example $3+5$ and $5+3$) are considered the same and counted once.

For example, when $n=24$ and $k=3$ there are 2 ways: $\{2, 3, 19\}$ and $\{2, 5, 17\}$. When $n=24$ and $k=2$ there are 3 ways: $\{5, 19\}$, $\{7, 17\}$, and $\{11, 13\}$. When $n=2$ and $k=1$ there is 1 way: $\{2\}$. When $n=1$ and $k=1$ the answer is 0 because 1 is not prime. Likewise, no two distinct primes sum to 4, so the answer for $n=4$, $k=2$ is also 0.

The first line contains the number of test cases $T$. Each test case is a single line containing two integers $n$ and $k$ separated by a space. ($n \le 1120$, $k \le 14$)

For each test case, print the number of ways on its own line. The answer is always less than $2^{31}$.