Clasificaciones Maratones PUJ

In the field of Cryptography, prime numbers play an important role. We are interested in a scheme called "Diffie-Hellman" key exchange which allows two communicating parties to exchange a secret key. This method requires a prime number p and r which is a primitive root of p to be publicly known. For a prime number p, r is a primitive root if and only if it's exponents r, r², r³ ... r^p-1 are distinct (mod p).

Cryptography Experts Group (CEG) is trying to develop such a system. They want to have a list of prime numbers and their primitive roots. You are going to write a program to help them. Given a prime number p and another integer r < p, you need to tell whether r is a primitive root of p.

Input

There will be multiple test cases. Each test case starts with two integers p (p < 2³¹) and n (1 ≤ n ≤ 100) separated by a space on a single line. p is the prime number we want to use and n is the number of candidates we need to check. Then n lines follow each containing a single integer to check. An empty line follows each test case and the end of test cases is indicated by p=0 and n=0 and it should not be processed. The number of test cases is at most 60.

Output

For each test case print "YES" (quotes for clarity) if r is a primitive root of p and "NO" (again quotes for clarity) otherwise.

Example

Input:
5 2
3
4

7 2
3
4

0 0

Output:
YES
NO
YES
NO

Explanation

In the first test case 3¹, 3² , 3³ and 3⁴ are respectively 3, 4, 2 and 1 (mod 5). So, 3 is a primitive root of 5.

4¹, 4² , 4³ and 4⁴ are respectively 4, 1, 4 and 1 respectively. So, 4 is not a primitive root of 5.