Initially, you have a set S={x,y}S=\{x,y\}S={x,y} (x≠y)(x \neq y )(x≠y). Then you have two operations:
∙\bullet∙ 1. Choose two elements a,b(a≠b)a,b (a \neq b)a,b(a≠b) from
set SSS, insert a−ba-ba−b to the set.
∙\bullet∙ 2. Choose two elements a,b(a≠b)a,b (a \neq b)a,b(a≠b) from
set SSS, insert gcd(∣a∣,∣b∣)\gcd(|a|,|b|)gcd(∣a∣,∣b∣) to the set.
We define ∣a∣|a|∣a∣ as the absolute value of aaa.
We define gcd(a, b)\gcd(a,\ b)gcd(a, b) as the greatest common divisor of aaa and bbb.
Specially, gcd(a, 0)=gcd(0, a)=a\gcd(a, \ 0) = \gcd(0,\ a) = agcd(a, 0)=gcd(0, a)=a.
You task is making z∈Sz \in Sz∈S after several operations.
If possible, print "YES". Otherwise, print "NO".