(1+a1*t+(a1*t)^2+(a1*t)^3......(a1*t)^d) * (1+a2*t+(a2*t)^2...+(a2*t)^d) * ... * (1+an*t+(an*t)^2...(an*t)^d)`

same as 
****(a1*t-1)^-1*(a2*t-1)^-1*..*(an*t-1)^-1****

anyone knows how to get t^d coefficient,d<=1e18

I was thinking of FFT but its dlog(d) which will give tle ,any approach or article where I could read more about polynomial multiplication