{"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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eKuroni is the coordinator of the next Mathforces round written by the \"Proof by AC\" team. All the preparation has been done, and he is discussing with the team about the score distribution for the round.\u003c/p\u003e\u003cp\u003eThe round consists of $$$n$$$ problems, numbered from $$$1$$$ to $$$n$$$. The problems are ordered in increasing order of difficulty, no two problems have the same difficulty. A score distribution for the round can be denoted by an array $$$a_1, a_2, \\dots, a_n$$$, where $$$a_i$$$ is the score of $$$i$$$-th problem. \u003c/p\u003e\u003cp\u003eKuroni thinks that the score distribution should satisfy the following requirements:\u003c/p\u003e\u003cul\u003e \u003cli\u003e The score of each problem should be a positive integer not exceeding $$$10^9$$$. \u003c/li\u003e\u003cli\u003e A harder problem should grant a strictly higher score than an easier problem. In other words, $$$1 \\leq a_1 \u0026lt; a_2 \u0026lt; \\dots \u0026lt; a_n \\leq 10^9$$$. \u003c/li\u003e\u003cli\u003e The \u003cspan class\u003d\"tex-font-style-bf\"\u003ebalance\u003c/span\u003e of the score distribution, defined as the number of triples $$$(i, j, k)$$$ such that $$$1 \\leq i \u0026lt; j \u0026lt; k \\leq n$$$ and $$$a_i + a_j \u003d a_k$$$, should be exactly $$$m$$$. \u003c/li\u003e\u003c/ul\u003e\u003cp\u003eHelp the team find a score distribution that satisfies Kuroni\u0027s requirement. In case such a score distribution does not exist, output $$$-1$$$.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first and single line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\le n \\le 5000$$$, $$$0 \\leq m \\leq 10^9$$$)\u0026nbsp;— the number of problems and the required balance.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eIf there is no solution, print a single integer $$$-1$$$.\u003c/p\u003e\u003cp\u003eOtherwise, print a line containing $$$n$$$ integers $$$a_1, a_2, \\dots, a_n$$$, representing a score distribution that satisfies all the requirements. If there are multiple answers, print any of them.\u003c/p\u003e"}},{"title":"Examples","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e5 3\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e4 5 9 13 18\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e8 0\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e10 11 12 13 14 15 16 17\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e4 10\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e-1\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003eIn the first example, there are $$$3$$$ triples $$$(i, j, k)$$$ that contribute to the balance of the score distribution. \u003c/p\u003e\u003cul\u003e \u003cli\u003e $$$(1, 2, 3)$$$ \u003c/li\u003e\u003cli\u003e $$$(1, 3, 4)$$$ \u003c/li\u003e\u003cli\u003e $$$(2, 4, 5)$$$ \u003c/li\u003e\u003c/ul\u003e"}}]}