Prime Factorization

Limits: 2 sec., 256 MiB

This statement was translated automatically from Ukrainian.

Zenyk is solving the following problem in his math class — he is given a set of prime numbers \(p_1, p_2, ..., p_k\) and a target number \(n\). His task is to determine whether \(n\) can be factored into primes using only the given prime numbers? Formally, you need to tell whether there exists a set of non-negative integers \(e_1, e_2, ..., e_k\) such that \(p_1^{e_1} \cdot p_2^{e_2} \cdot ... \cdot p_k^{e_k} = n\).

Input

The first line contains two numbers \(n\) and \(k\). The second line contains \(k\) prime numbers \(p_i\) separated by a space.

Output

Output YES if such a factorization is possible, otherwise output NO.

Constraints

\(2 \leq n \leq 10^9\),

\(1 \leq k \leq 100\),

\(1 \leq p_i \leq 10^9\),

\(p_i\) is prime.

Samples

Input (stdin) сopy	Output (stdout) сopy
12 3 2 3 7	YES

Input (stdin) сopy	Output (stdout) сopy
15 5 7 11 13 3 11	NO

Notes

In the first test, \(2^2 \cdot 3^1 \cdot 7^0 = 12\).