{"raw_statement":[{"iden":"problem statement","content":"You are given positive integers $N$ and $K$.\nAn integer sequence of length $N$ where all elements are between $1$ and $2^K - 1$, inclusive, is called a **good sequence**.\nThe **score** of a good sequence $A=(A_1,A_2,\\ldots,A_N)$ is defined as follows:\n\n*   The number of distinct integers that can be expressed as $\\displaystyle \\left\\lfloor\\frac{A_i}{2^k} \\right\\rfloor$ using an integer $i$ between $1$ and $N$, inclusive, and a non-negative integer $k$.\n\nFor example, for $A=(3,5)$, five integers can be expressed as $\\displaystyle \\left\\lfloor\\frac{A_i}{2^k} \\right\\rfloor$: $0$, $1$, $2$, $3$, and $5$, so the score is $5$.\nFind one good sequence with the maximum score.\nFor each input file, you are given $T$ test cases to solve."},{"iden":"constraints","content":"*   $1 \\leq T \\leq 10^5$\n*   $1 \\leq N \\leq 10^5$\n*   $1 \\leq K \\leq 30$\n*   The sum of $N$ across the test cases in a single input file is at most $2 \\times 10^5$.\n*   All input values are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format. Here, $\\text{case}_i$ denotes the $i$\\-th test case.\n\n$T$\n$\\mathrm{case}_1$\n$\\mathrm{case}_2$\n$\\vdots$\n$\\mathrm{case}_T$\n\nEach test case is given in the following format:\n\n$N$ $K$"},{"iden":"sample input 1","content":"3\n3 3\n7 2\n8 20"},{"iden":"sample output 1","content":"5 6 7\n2 2 3 3 1 3 3\n662933 967505 876482 840117 1035841 651549 543175 781219\n\nConsider the first test case.\nFor $A=(5,6,7)$, seven integers can be expressed as $\\displaystyle \\left\\lfloor\\frac{A_i}{2^k} \\right\\rfloor$: $0$, $1$, $2$, $3$, $5$, $6$, and $7$, so its score is $7$.\nOutputs such as $A=(7,4,5)$ and $A=(6,5,4)$ would also be accepted."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}