Let N be the sum of all binomial coefficients \binom{a}{b} such that a and b are nonnegative integers and a+b is an even integer less than 100. Find the remainder when N is divided by 144 . (Note: \binom{a}{b}=0 if a<b, and \binom{0}{0}=1.)
Let N be the sum of all binomial coefficients \binom{a}{b} such that a and b are nonnegative integers and a+b is an even integer less than 100. Find the remainder when N is divided by 144 . (Note: \binom{a}{b}=0 if a<b, and \binom{0}{0}=1.)