Problem Statement

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:

• Choose black or white with equal probability, and eat a piece of that color if it exists.

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.

Input

Input is given from Standard Input in the following format:
B W

Output

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.

Constraints

• All values in input are integers.
• $1 \leq B,W \leq 10^{5}$

Sample Input 1

2 1

Sample Output 1

500000004
750000006
750000006

• There are three possible orders in which Snuke eats the pieces:
• white, black, black
• black, white, black

• black, black, white

• with probabilities $\frac{1}{2}, \frac{1}{4}, \frac{1}{4},$ respectively. Thus, the probabilities of eating a black piece first, second and third are $\frac{1}{2},\frac{3}{4}$ and $\frac{3}{4},$ respectively.

Sample Input 2

3 2

Sample Output 2

500000004
500000004
625000005
187500002
187500002

• They are $\frac{1}{2},\frac{1}{2},\frac{5}{8},\frac{11}{16}$ and $\frac{11}{16},$ respectively.

Sample Input 3

6 9

Sample Output 3

500000004
500000004
500000004
500000004
500000004
500000004
929687507
218750002
224609377
303710940
633300786
694091802
172485353
411682132
411682132

见题面 Input 部分

见题面 Output 部分