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문제

Little Bobby Tables stores his favorite big numbers in his database. Those numbers take a lot of memory, so he is trying to figure out a way to store them more efficiently. He noticed that in the database there is a number $X$ which has no large prime factors, and he suspects that it is of the form $n \choose k$, for some relatively small numbers $n$, $k$.

Help Bobby and check if it is really the case. Given an integer $m$ and the prime factorization of $X$, determine whether there exist integers $n$, $k$ such that $0 \le k \le n \le m$ and $X = {n \choose k}$.

입력

The first line of input contains the number of test cases $z$ ($1 \le z \le 10\,000$). The descriptions of the test cases follow.

The first line of every test case contains two integers $t, m$ ($1 \le t, m \le 150\,000$), the number of primes in the factorization of $X$ and the upper bound for output values, respectively. The second line contains $t$ primes $p_i$ ($2 \le p_i \le m$), such that product of all $p_i$ is $X$.

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

출력

For each test case, if there exist appropriate $n$ and $k$, output "YES" in the first line, and the values of $n$ and $k$ in the second line. Otherwise output only one line containing "NO".

예제 입력 1

2
2 5
3 2
3 7
2 2 2

예제 출력 1

YES
4 2
NO