{"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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eLet\u0027s define a function $$$f(p)$$$ on a permutation $$$p$$$ as follows. Let $$$g_i$$$ be the \u003ca href\u003d\"https://en.wikipedia.org/wiki/Greatest_common_divisor\"\u003egreatest common divisor (GCD)\u003c/a\u003e of elements $$$p_1$$$, $$$p_2$$$, ..., $$$p_i$$$ (in other words, it is the GCD of the prefix of length $$$i$$$). Then $$$f(p)$$$ is the number of \u003cspan class\u003d\"tex-font-style-bf\"\u003edistinct\u003c/span\u003e elements among $$$g_1$$$, $$$g_2$$$, ..., $$$g_n$$$.\u003c/p\u003e\u003cp\u003eLet $$$f_{max}(n)$$$ be the maximum value of $$$f(p)$$$ among all permutations $$$p$$$ of integers $$$1$$$, $$$2$$$, ..., $$$n$$$.\u003c/p\u003e\u003cp\u003eGiven an integers $$$n$$$, count the number of permutations $$$p$$$ of integers $$$1$$$, $$$2$$$, ..., $$$n$$$, such that $$$f(p)$$$ is equal to $$$f_{max}(n)$$$. Since the answer may be large, print the remainder of its division by $$$1000\\,000\\,007 \u003d 10^9 + 7$$$.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe only line contains the integer $$$n$$$ ($$$2 \\le n \\le 10^6$$$)\u0026nbsp;— the length of the permutations.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eThe only line should contain your answer modulo $$$10^9+7$$$.\u003c/p\u003e"}},{"title":"Examples","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e3\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e4\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e6\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e120\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003eConsider the second example: these are the permutations of length $$$3$$$:\u003c/p\u003e\u003cul\u003e \u003cli\u003e $$$[1,2,3]$$$, $$$f(p)\u003d1$$$. \u003c/li\u003e\u003cli\u003e $$$[1,3,2]$$$, $$$f(p)\u003d1$$$. \u003c/li\u003e\u003cli\u003e $$$[2,1,3]$$$, $$$f(p)\u003d2$$$. \u003c/li\u003e\u003cli\u003e $$$[2,3,1]$$$, $$$f(p)\u003d2$$$. \u003c/li\u003e\u003cli\u003e $$$[3,1,2]$$$, $$$f(p)\u003d2$$$. \u003c/li\u003e\u003cli\u003e $$$[3,2,1]$$$, $$$f(p)\u003d2$$$. \u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThe maximum value $$$f_{max}(3) \u003d 2$$$, and there are $$$4$$$ permutations $$$p$$$ such that $$$f(p)\u003d2$$$.\u003c/p\u003e"}}]}