human
Give me a Python code to determine whether the Gauls should wait for the black day after today's victory of Asterix and Obelix given the following:
A prime number is a number which has exactly two distinct divisors: one and itself. For example, numbers 2, 7, 3 are prime, and 1, 6, 4 are not.

The next prime number after x is the smallest prime number greater than x. For example, the next prime number after 2 is 3, and the next prime number after 3 is 5. Note that there is exactly one next prime number after each number. So 5 is not the next prime number for 2.

One cold April morning Panoramix predicted that soon Kakofonix will break free from his straitjacket, and this will be a black day for the residents of the Gallic countryside.

Panoramix's prophecy tells that if some day Asterix and Obelix beat exactly x Roman soldiers, where x is a prime number, and next day they beat exactly y Roman soldiers, where y is the next prime number after x, then it's time to wait for Armageddon, for nothing can shut Kakofonix up while he sings his infernal song.

Yesterday the Gauls beat n Roman soldiers and it turned out that the number n was prime! Today their victims were a troop of m Romans (m > n). Determine whether the Gauls should wait for the black day after today's victory of Asterix and Obelix?

Input

The first and only input line contains two positive integers — n and m (2 ≤ n < m ≤ 50). It is guaranteed that n is prime.

Pretests contain all the cases with restrictions 2 ≤ n < m ≤ 4.

Output

Print YES, if m is the next prime number after n, or NO otherwise.

Examples

Input

3 5

Output

YES

Input

7 11

Output

YES

Input

7 9

Output

NO
Using python3 can you solve the prior task?
assistant
#Here is Python code to determine whether the Gauls should wait for the black day after today's victory of Asterix and Obelix.

def test():
    def is_prime(n):
        if n == 2:
            return True
        if n%2 == 0:
            return False
        k = int(n**0.5)
        k = k-1 if k%2 == 0 else k
        for i in range(k, 1, -2):
            if n % i == 0:
                return False
        return True
    n, m = input().split()
    nex = int(n) + 1
    while True:
        if is_prime(nex):
            if nex == int(m):
                print("YES")
            else:
                print("NO")
            break
        nex += 1

if __name__ == "__main__":
    test()