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.

Constraints

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

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.

Examples

Input

2 1

Output

500000004
750000006
750000006

Input

3 2

Output

500000004
500000004
625000005
187500002
187500002

Input

6 9

Output

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

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见题面