{"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\"\u003eThere are $n$ groups of coins, and the $i$-th group contains two coins valued at $a_i$ and $b_i$. Now you want to pick exactly $k$ coins out of them. However, there is a restriction - you can not pick the second coin valued at $b_i$ in the $i$-th group without picking the other one in the same group. In other words, in the $i$-th group, you can\u003cbr\u003e- pick none of the two coins;\u003cbr\u003e- pick only the first one valued at $a_i$; or\u003cbr\u003e- pick both of them. \u003cbr\u003e\u003cbr\u003eWe now want to know the maximum sum of the $k$ picked coins\u0027 values, denoted by $f(k)$. \u003cbr\u003e\u003cbr\u003eFurthermore, we want to know $f(1), f(2), \\cdots, f(2n)$.\u003cbr\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The input contains several test cases, and the first line contains a single integer $T~(1 \\le T \\le 90)$, the number of test cases.\u003cbr\u003e\u003cbr\u003eFor each test case, the first line contains an integer $n~(1 \\le n \\le 100\\,000)$, indicating the number of coin groups.\u003cbr\u003e\u003cbr\u003eEach of the following $n$ lines contains two integers $a_i,b_i~(1 \\le a_i, b_i \\le 10\\,000)$ indicating the coin values in that group.\u003cbr\u003e\u003cbr\u003eIt is guaranteed that the sum of $n$ in all test cases does not exceed $2\\,100\\,000$.\u003cbr\u003e"}},{"title":"Output","value":{"format":"HTML","content":"For each test group, just output $2n$ integers in a single line representing $f(1), f(2), \\cdots, f(2n)$, and adjacent integers should be separated by one space.\u003cbr\u003e"}},{"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 2\r\n1 4\r\n4 2\r\n2\r\n1 3\r\n3 2\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e4 6 9 11 12 14\r\n3 5 7 9\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}