B'Vasilije is a smart student and his discrete mathematics teacher Sonja taught him number theory very well. He gave Ognjen a positive integer n . Denote d(n) as the number of positive integer divisors of n , and denote gcd(a, b) as the largest integer g such that a is divisible by g and b is divisible by g . After that, he gave Ognjen q queries, and there are 2 types of queries. Note that n does not get back to its initial value after the type 1 query. Since Ognjen is afraid of number theory, Vasilije promised him that after each query, d(n) <= 10^9 , however, even with that constraint, he still needs your help with this problem. The first line contains a positive integer t , ( 1 <= t <= 100 ) -- the number of test cases. The first line of each test case contains 2 integers, n and q ( 1 <= n <= 10^{6} , 1 <= q <= 1000 ) -- the number n and the number of queries. The following q lines contain an integer k ( 1 <= k <= 2 ), if k=1 then there is another integer in this line x ( 1 <= x <= 10^6 ) -- the description of the queries. It is guaranteed that, for the given input, d(n) does not exceed 10^9 at any point. It is guaranteed that the sum of q over all test cases doesn 't exceed 10^3 . For each type 1 query, you should output "YES" if there exist such positive integer a that gcd(a, n) = 1 and d(n cdot a)=n , and "NO" if he can 't. You can output the answer in any case (for example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as a positive answer). In the first test case, we initially have n=1 . After the first query: n=1 , d(n)=1 , so by taking a = 1 , d(n cdot a) = n , and the answer to this query is "YES". After the second query: n=2 , d(n)=2 , we can, again, take a = 1 , d(n cdot a) = n , and'...