Bobby Tables
Little Bobby Tables stores his favourite 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 Ck_n, 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 ≤ k ≤ n ≤ m and X = Ck_n.
A binomial coefficient Ck_n is a number
Input
The first line contains the number of test cases z (1 ≤ z ≤ 10 000). The descriptions of the testcases follow.
The first line of every test case contains two integers t, m (1 ≤ t, m ≤ 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 ≤ p[i] ≤ m), such that product of all pi 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.
Output
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".