For a positive integer $n$, the $n^{th}$ triangular number is $T(n)=\dfrac{n(n+1)}{2}.$ For example, $T(3) = \frac{3(3+1)}{2}= \frac{3(4)}{

For a positive integer $n$, the $n^{th}$ triangular number is $T(n)=\dfrac{n(n+1)}{2}.$

For example, $T(3) = \frac{3(3+1)}{2}= \frac{3(4)}{2}=6$, so the third triangular number is 6.

Determine the smallest integer $b>2011$ such that $T(b+1)-T(b)=T(x)$ for some positive integer .