{"trustable":true,"prependHtml":"\u003cstyle type\u003d\u0027text/css\u0027\u003e\n .input, .output {\n border: 1px solid #888888;\n }\n .output {\n margin-bottom: 1em;\n position: relative;\n top: -1px;\n }\n .output pre, .input pre {\n background-color: #EFEFEF;\n line-height: 1.25em;\n margin: 0;\n padding: 0.25em;\n }\n \u003c/style\u003e\n \u003clink rel\u003d\"stylesheet\" href\u003d\"//codeforces.org/s/96598/css/problem-statement.css\" type\u003d\"text/css\" /\u003e\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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eThere are $$$n$$$ points on a horizontal line, labelled with $$$1$$$ through $$$n$$$ from left to right.\u003c/p\u003e\u003cp\u003eThe distance between the $$$i$$$-th point and the $$$(i + 1)$$$-th point is $$$a_i$$$.\u003c/p\u003e\u003cp\u003eFor each integer $$$k$$$ ranged from $$$1$$$ to $$$n$$$, you are asked to select exactly $$$k$$$ different given points on the line to maximize the sum of distances between all pairs of selected points.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe input contains several test cases, and the first line contains a positive integer $$$T$$$ indicating the number of test cases which is up to $$$1000$$$.\u003c/p\u003e\u003cp\u003eFor each test case, the first line contains an integer $$$n$$$ indicating the number of points, where $$$2 \\leq n \\leq 10^5$$$.\u003c/p\u003e\u003cp\u003eThe second line contains $$$(n - 1)$$$ positive integers $$$a_1, a_2, \\cdots, a_{n - 1}$$$, where $$$1 \\leq a_i \\leq 10^4$$$.\u003c/p\u003e\u003cp\u003eWe guarantee that the sum of $$$n$$$ in all test cases is up to $$$10^6$$$.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eFor each test case, output a line containing $$$n$$$ integers, the $$$i$$$-th of which is the maximum sum of distances in case $$$k \u003d i$$$. You should output exactly one whitespace between every two adjacent numbers and avoid any trailing whitespace in this line.\u003c/p\u003e"}},{"title":"Examples","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e1\n5\n2 3 1 4\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e0 10 20 34 48\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003eThe figure below describes the sample test case.\u003c/p\u003e\u003ccenter\u003e \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/1765bec6bd7b504d7322a29fbbed0164?v\u003d1715838255\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e \u003c/center\u003e\u003cp\u003eThe only best selection for $$$k \u003d 2$$$ should choose the leftmost and the rightmost points, while a possible best selection for $$$k \u003d 3$$$ could contain any extra point in the middle.\u003c/p\u003e"}}]}