Bobby Tables

Little Bobby Tables stores his favorite big numbers in his database. Those numbers take a lot of memory, so he is trying to find a more efficient way to store them.

The database holds a number $X$ with no large prime factors. Bobby suspects that $X$ has the form $X = \binom{n}{k}$ for some relatively small integers $n$ and $k$.

Given an integer $m$ and the prime factorization of $X$, determine whether there exist integers $n$ and $k$ such that $0 \le k \le n \le m$ and $X = \binom{n}{k}$.

The first line contains the number of test cases $z$ ($1 \le z \le 10\,000$). Each test case is described as follows.

The first line of a test case contains two integers $t$ and $m$ ($1 \le t, m \le 150\,000$), where $t$ is the number of primes in the factorization of $X$ and $m$ is the upper bound for the output values.

The second line contains $t$ primes $p_1, \ldots, p_t$ ($2 \le p_i \le m$) whose product is $X$.

The sum of $t$ over all test cases does not exceed $200\,000$. The sum of $m$ over all test cases does not exceed $2\,000\,000$.

For each test case, if there exist suitable $n$ and $k$, print "YES" on the first line and the values of $n$ and $k$ on the second line. Otherwise, print only "NO" on one line.