{"raw_statement":[{"iden":"problem statement","content":"Today, Snuke will eat $B$ pieces of black chocolate and $W$ pieces of white chocolate for an afternoon snack.\nHe will repeat the following procedure until there is no piece left:\n\n*   Choose black or white with equal probability, and eat a piece of that color if it exists.\n\nFor 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."},{"iden":"notes","content":"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 $xz \\equiv y \\pmod{10^9 + 7}$."},{"iden":"constraints","content":"*   All values in input are integers.\n*   $1 \\leq B,W \\leq 10^{5}$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$B$ $W$"},{"iden":"sample input 1","content":"2 1"},{"iden":"sample output 1","content":"500000004\n750000006\n750000006\n\n*   There are three possible orders in which Snuke eats the pieces:\n    *   white, black, black\n    *   black, white, black\n    *   black, black, white\n*   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."},{"iden":"sample input 2","content":"3 2"},{"iden":"sample output 2","content":"500000004\n500000004\n625000005\n187500002\n187500002\n\n*   They are $\\frac{1}{2},\\frac{1}{2},\\frac{5}{8},\\frac{11}{16}$ and $\\frac{11}{16}$, respectively."},{"iden":"sample input 3","content":"6 9"},{"iden":"sample output 3","content":"500000004\n500000004\n500000004\n500000004\n500000004\n500000004\n929687507\n218750002\n224609377\n303710940\n633300786\n694091802\n172485353\n411682132\n411682132"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}