An up-right path is a sequence of points $\mathbf { a } _ { 0 } = \left( x _ { 0 } , y _ { 0 } \right) , \mathbf { a } _ { 1 } = \left( x _ { 1 } , y _ { 1 } \right) , \mathbf { a } _ { 2 } = ( x _ { 2 } , y _ { 2 } ), \ldots$ such that $\mathbf { a } _ { i + 1 } - \mathbf { a } _ { i }$ is either $( 1,0 )$ or $( 0,1 )$. The number of up-right paths from $( 0,0 )$ to $( 100,100 )$ which pass through $( 1,2 )$ is:\\
(A) $3 \cdot \binom { 197 } { 99 }$\\
(B) $3 \cdot \binom { 100 } { 50 }$\\
(C) $2 \cdot \binom { 197 } { 98 }$\\
(D) $3 \cdot \binom { 197 } { 100 }$.