{"trustable":true,"prependHtml":"\u003cscript\u003e window.katexOptions \u003d { disable: true }; \u003c/script\u003e\n\u003cscript type\u003d\"text/x-mathjax-config\"\u003e\n MathJax.Hub.Config({\n tex2jax: {\n inlineMath: [[\u0027$$$\u0027,\u0027$$$\u0027], [\u0027$\u0027,\u0027$\u0027]],\n displayMath: [[\u0027$$$$$$\u0027,\u0027$$$$$$\u0027], [\u0027$$\u0027,\u0027$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\" type\u003d\"text/javascript\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"panel_content\"\u003eAs we know, Rikka is poor at math. Yuta is worrying about this situation, so he gives Rikka some math tasks to practice. There is one of them:\u003cbr\u003e\u003cbr\u003eYuta has n numbers A[1]~A[n] and a number K. For any none empty subset S of the numbers, the value of S is equal to the sum of the largest min(|S|,k) numbers in S. The value of the array A is equal to the sum of the value of all none empty subset of the numbers. \u003cbr\u003e\u003cbr\u003eNow Yuta shows the n numbers, And he wants to know the value of the array for each K in [1,n]. \u003cbr\u003e\u003cbr\u003eIt is too difficult for Rikka. Can you help her?\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line contains a number t(1\u0026lt;\u003dt\u0026lt;\u003d10), the number of the testcases.\u003cbr\u003e\u003cbr\u003eFor each testcase, the first line contains a number n(1\u0026lt;\u003dn\u0026lt;\u003d100000), the number of numbers Yuta has. The second line contains n number A[1]~A[n](0\u0026lt;\u003dA[i]\u0026lt;\u003d10^9)."}},{"title":"Output","value":{"format":"HTML","content":"For each testcase, print a line contains exactly n numbers, the ith number is the value of the array when K\u003di. The answer may be very large, so you only need to print the answer module 998244353."}},{"title":"Sample","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e2\r\n3\r\n1 1 1\r\n5\r\n1 2 3 4 5\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e7 11 12\r\n129 201 231 239 240\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}