Cool Multiplications

Level pending

$A = 1^2 \times 2^2 \times 3^2\times 4^2\times 5^2\times 6^2\times 7^2\times 8^2\times 9^2\times 10^2$

$B = 1! \times 2! \times 3!\times 4!\times 5!\times 6!\times 7!\times 8!\times 9!\times 10!$

$C = A\times B$

The last three digits of $C$ are $a, b, c$ respectively

What is $a\times b\times c$ ?