Magical Numbers!

Let's define 'Magical Number' !

A Magical Number P is a decimal number consisting of 2n digits with the properties that

(I) No digit of P is 0 (Zero);

(II) Sum of the digits of P is equal to A and

(III) Product of the digits of P equals B ,

where and n is a natural number.

For example, for P =1236 with A =12 and B =36, Sum of Digits of P=1+2+3+6=12=A and Product of digits of P=1×2×3×6=36=B . Yeah, 1236 is a Magical Number.

You have to find out the number of Magical numbers greater than 1236 and less than 1 Billion.