Score : 700 points
Today, Snuke will eat B pieces of black chocolate and W pieces of white chocolate for an afternoon snack.
He will repeat the following procedure until there is no piece left:
For each integer i from 1 to B+W (inclusive), find the probability that the color of the i-th piece to be eaten is black. It can be shown that these probabilities are rational, and we ask you to print them modulo 10^9 + 7, as described in Notes.
When you print a rational number, first write it as a fraction \frac{y}{x}, where x, y are integers and x is not divisible by 10^9 + 7 (under the constraints of the problem, such representation is always possible). Then, you need to print the only integer z between 0 and 10^9 + 6, inclusive, that satisfies xz \equiv y \pmod{10^9 + 7}.
Input is given from Standard Input in the following format:
B W
Print the answers in B+W lines. In the i-th line, print the probability that the color of the i-th piece to be eaten is black, modulo 10^{9}+7.
2 1
500000004 750000006 750000006
3 2
500000004 500000004 625000005 187500002 187500002
6 9
500000004 500000004 500000004 500000004 500000004 500000004 929687507 218750002 224609377 303710940 633300786 694091802 172485353 411682132 411682132