Let m be the number of solutions in positive integers to the equation 4 x+3 y+2 z=2009, and

let n be the number of solutions in positive integers to the equation 4 x+3 y+2 z=2000.

Find the remainder when m-n is divided by 1000.

let n be the number of solutions in positive integers to the equation 4 x+3 y+2 z=2000.

Find the remainder when m-n is divided by 1000.