From the sequence \( \space2^1, 2^2 \times 3^1, 2^3 \times 3^2, \dots, 2^k \times 3^{k-1} \), you have to select some numbers. The product of the selected numbers will be used as the numerator of a fraction. The product of the remaining numbers will be the denominator of the fraction. You want the value of the fraction to be \( 1 \). How many numbers between \( 2001 \) and \( 2100 \) make this possible?