Balls in the boxes

We have several blue balls and red balls and we want to put them into boxes.

The rules for placing the balls into boxes are described below.

• Each box contains at least 2 balls and at most 6 balls.
• Each box contains at least 1 red ball and at most 4 blue balls.
• Balls are different from each other, even they have the same color.
• The order of the box doesn't matter. The order of each ball in the box doesn't matter.

For example, if we have 3 blue balls and 2 red balls. There are 7 different ways to put them into boxes.

(1). {B1,R1}, {B2,B3,R2}
(2). {B1,R2}, {B2,B3,R1}
(3). {B2,R1}, {B1,B3,R2}
(4). {B2,R2}, {B1,B3,R1}
(5). {B3,R1}, {B1,B2,R2}
(6). {B3,R2}, {B1,B2,R1}
(7). {B1,B2,B3,R1,R2}

Let $W(B,R)$ be the number of different ways to place B blue balls and R red balls into the boxes.

You are given $W(3,2)=7$, $W(5,4)=1510$ and $W(31,27)\equiv 336072473(\mathrm{mod}1000000007)$

Find $W(3141,2718)mod1000000007$