{"raw_statement":[{"iden":"problem statement","content":"We say that a set $S$ of positive integers is _good_ when, for any $a,\\ b \\in S\\ (a\\neq b)$, $b$ is not a multiple of $a$.\nYou are given a set of $N$ integers between $1$ and $2M$ (inclusive): $S=\\lbrace A_1,\\ A_2,\\ \\dots,\\ A_N\\rbrace$.\nFor each $i=1,\\ 2,\\ \\dots,\\ N$, determine whether there exists a good set with $M$ elements that is a subset of $S$ containing $A_i$."},{"iden":"constraints","content":"*   $M \\leq N \\leq 2M$\n*   $1 \\leq M \\leq 3 \\times 10^5$\n*   $1 \\leq A_1 < A_2 < \\dots < A_N \\leq 2M$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$\n$A_1$ $A_2$ $\\dots$ $A_{N}$"},{"iden":"sample input 1","content":"5 3\n1 2 3 4 5"},{"iden":"sample output 1","content":"No\nYes\nYes\nYes\nYes\n\nTrivially, the only good set containing $A_1=1$ is $\\lbrace 1\\rbrace$, which has just one element, so the answer for $i=1$ is `No`.\nThere is a good set $\\lbrace 2,\\ 3,\\ 5\\rbrace$ containing $A_2=2$, so the answer for $i=2$ is `Yes`."},{"iden":"sample input 2","content":"4 4\n2 4 6 8"},{"iden":"sample output 2","content":"No\nNo\nNo\nNo"},{"iden":"sample input 3","content":"13 10\n2 3 4 6 7 9 10 11 13 15 17 19 20"},{"iden":"sample output 3","content":"No\nNo\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nNo"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}