{"raw_statement":[{"iden":"problem statement","content":"You are going to hold a competition of one-to-one game called AtCoder Janken. _(Janken is the Japanese name for Rock-paper-scissors.)_ $N$ players will participate in this competition, and they are given distinct integers from $1$ through $N$. The arena has $M$ playing fields for two players. You need to assign each playing field two distinct integers between $1$ and $N$ (inclusive). You cannot assign the same integer to multiple playing fields. The competition consists of $N$ rounds, each of which proceeds as follows:\n\n*   For each player, if there is a playing field that is assigned the player's integer, the player goes to that field and fight the other player who comes there.\n*   Then, each player adds $1$ to its integer. If it becomes $N+1$, change it to $1$.\n\nYou want to ensure that no player fights the same opponent more than once during the $N$ rounds. Print an assignment of integers to the playing fields satisfying this condition. It can be proved that such an assignment always exists under the constraints given."},{"iden":"constraints","content":"*   $1 \\leq M$\n*   $M \\times 2 +1 \\leq N \\leq 200000$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$"},{"iden":"sample input 1","content":"4 1"},{"iden":"sample output 1","content":"2 3\n\nLet us call the four players A, B, C, and D, and assume that they are initially given the integers $1$, $2$, $3$, and $4$, respectively.\n\n*   The $1$\\-st round is fought by B and C, who has the integers $2$ and $3$, respectively. After this round, A, B, C, and D have the integers $2$, $3$, $4$, and $1$, respectively.\n    \n*   The $2$\\-nd round is fought by A and B, who has the integers $2$ and $3$, respectively. After this round, A, B, C, and D have the integers $3$, $4$, $1$, and $2$, respectively.\n    \n*   The $3$\\-rd round is fought by D and A, who has the integers $2$ and $3$, respectively. After this round, A, B, C, and D have the integers $4$, $1$, $2$, and $3$, respectively.\n    \n*   The $4$\\-th round is fought by C and D, who has the integers $2$ and $3$, respectively. After this round, A, B, C, and D have the integers $1$, $2$, $3$, and $4$, respectively.\n    \n\nNo player fights the same opponent more than once during the four rounds, so this solution will be accepted."},{"iden":"sample input 2","content":"7 3"},{"iden":"sample output 2","content":"1 6\n2 5\n3 4"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}