{"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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eYou are given two integers $$$n$$$ and $$$d$$$. You need to construct a rooted binary tree consisting of $$$n$$$ vertices with a root at the vertex $$$1$$$ and the sum of depths of all vertices equals to $$$d$$$.\u003c/p\u003e\u003cp\u003eA tree is a connected graph without cycles. A rooted tree has a special vertex called the root. A parent of a vertex $$$v$$$ is the last different from $$$v$$$ vertex on the path from the root to the vertex $$$v$$$. The depth of the vertex $$$v$$$ is the length of the path from the root to the vertex $$$v$$$. Children of vertex $$$v$$$ are all vertices for which $$$v$$$ is the parent. The binary tree is such a tree that no vertex has more than $$$2$$$ children.\u003c/p\u003e\u003cp\u003eYou have to answer $$$t$$$ independent test cases.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line of the input contains one integer $$$t$$$ ($$$1 \\le t \\le 1000$$$) — the number of test cases.\u003c/p\u003e\u003cp\u003eThe only line of each test case contains two integers $$$n$$$ and $$$d$$$ ($$$2 \\le n, d \\le 5000$$$) — the number of vertices in the tree and the required sum of depths of all vertices.\u003c/p\u003e\u003cp\u003eIt is guaranteed that the sum of $$$n$$$ and the sum of $$$d$$$ both does not exceed $$$5000$$$ ($$$\\sum n \\le 5000, \\sum d \\le 5000$$$).\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eFor each test case, print the answer.\u003c/p\u003e\u003cp\u003eIf it is impossible to construct such a tree, print \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eNO\u003c/span\u003e\" (without quotes) in the first line. Otherwise, print \"{YES}\" in the first line. Then print $$$n-1$$$ integers $$$p_2, p_3, \\dots, p_n$$$ in the second line, where $$$p_i$$$ is the parent of the vertex $$$i$$$. Note that the sequence of parents you print should describe some binary tree.\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\u003e3\n5 7\n10 19\n10 18\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eYES\n1 2 1 3 \nYES\n1 2 3 3 9 9 2 1 6 \nNO\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\u003ePictures corresponding to the first and the second test cases of the example:\u003c/p\u003e\u003cp\u003e\u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/37f1d44f4f9af65ea73e9e16e72ecca2?v\u003d1715622123\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u003c/p\u003e\u003cp\u003e\u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/99541a35036b1893c2833598c7057442?v\u003d1715622123\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u003c/p\u003e"}}]}