{"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\"\u003eDeclare:\u003cbr\u003e$k\u003d\\sum_{i\u003d1}^{m} \\varphi (i*n)\\ mod\\ 1000000007$\u003cbr\u003e\u003cbr\u003e$n$ is a square-free number.\u003cbr\u003e\u003cbr\u003e$\\varphi $ is the \u003cb\u003eEuler\u0027s totient function\u003c/b\u003e.\u003cbr\u003e\u003cbr\u003efind:\u003cbr\u003e$ans\u003dk^{k^{k^{k^{...^k}}}}\\ mod \\ p$\u003cbr\u003e\u003cbr\u003eThere are infinite number of $k$\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"Multiple test cases(test cases $\\leq 100$), one line per case.\u003cbr\u003e\u003cbr\u003eEach line contains three integers, $n, m$ and $p$.\u003cbr\u003e\u003cbr\u003e$1 \\leq n, m, p \\leq 10^{7}$\u003cbr\u003e"}},{"title":"Output","value":{"format":"HTML","content":"For each case, output a single line with one integer, ans."}},{"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\u003e1 2 6\r\n1 100 9\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e4\r\n7\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}