已知平面向量 $\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}$ 满足 $|\boldsymbol{a}|=|\boldsymbol{b}|=|\boldsymbol{a}-\boldsymbol{b}|=1, \boldsymbol{c} \cdot \boldsymbol{a}=\boldsymbol{c} \cdot \boldsymbol{b}=1$, 则 $|\boldsymbol{c}|=$
$\text{A.}$
$\text{B.}$
$\text{C.}$
$\text{D.}$