已知平面向量$$ \stackrel{\text{⃗}}{a}=\left(2,m\right)$$,$$ \stackrel{\text{⃗}}{b}=\left(1,-\sqrt[]{2}\right)$$,且$$ \left|2\stackrel{\text{⃗}}{a}-\stackrel{\text{⃗}}{b}\right|=\left|2\stackrel{\text{⃗}}{a}+\stackrel{\text{⃗}}{b}\right|$$,则$$ m=$$( )

A.1

B.2

C.$$ \sqrt[]{2}$$

D.4