{"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\"\u003eRecently, Mr. Frog has learned binary indexed tree. Here is the code of adding t to the interval [1,x]:\u003cbr\u003e\u003cpre\u003e\u003cbr\u003e void add (int x, int t ){\u003cbr\u003e for (int i \u003d x; i !\u003d 0; i -\u003d i \u0026amp; (-i))\u003cbr\u003e a[i] +\u003d t;\u003cbr\u003e }\u003cbr\u003e\u003c/pre\u003e\u003cbr\u003e\u003cbr\u003eIf Mr. Frog is required to add t to the interval [l,r], he will add(r,t), and then add(l - 1,-t).\u003cbr\u003e\u003cbr\u003eThe cost of an interval [l,r] is defined as the number of the “really changed point”. The “really changed point” is the point whose value is modified by the given code.\u003cbr\u003e\u003cbr\u003eFor example, in order to add 1 to the interval [6,6], Mr. Frog will add 1 to the interval [1,6] (a[6] and a[4] will be added by 1), and add -1 to the interval [1,5] (a[5] and a[4] will be added by -1).\u003cbr\u003e\u003cbr\u003eAs the result, a[6] will be added by 1, a[5] will be added by -1, and a[4] will be added by 0. a[6] and a[5] are “really changed point”, and the cost is 2.\u003cbr\u003e\u003cbr\u003eMr. Frog wants to calculate the sum of the cost of the interval [l,r]$\\subseteq $ \u0026#x12; [1,n] where l and r are two integers. Help Mr. Frog solve the problem.\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line contains only one integer T ($T\\leq 10000$), which indicates the number of test cases.\u003cbr\u003e\u003cbr\u003eFor each test case, it contains an integer n ($1\\leq n\\leq 10^{18}$)."}},{"title":"Output","value":{"format":"HTML","content":"For each test case, output one line ”Case #x: y”, where x is the case number (starting from 1), y is the sum of the cost (modulo 1000000007)."}},{"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\u003e3\r\n1\r\n2\r\n3\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eCase #1: 1\r\nCase #2: 4\r\nCase #3: 10\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}