{"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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eMakoto has a big blackboard with a positive integer $$$n$$$ written on it. He will perform the following action exactly $$$k$$$ times:\u003c/p\u003e\u003cp\u003eSuppose the number currently written on the blackboard is $$$v$$$. He will randomly pick one of the divisors of $$$v$$$ (possibly $$$1$$$ and $$$v$$$) and replace $$$v$$$ with this divisor. As Makoto uses his famous random number generator (RNG) and as he always uses $$$58$$$ as his generator seed, each divisor is guaranteed to be chosen with equal probability.\u003c/p\u003e\u003cp\u003eHe now wonders what is the expected value of the number written on the blackboard after $$$k$$$ steps.\u003c/p\u003e\u003cp\u003eIt can be shown that this value can be represented as $$$\\frac{P}{Q}$$$ where $$$P$$$ and $$$Q$$$ are coprime integers and $$$Q \\not\\equiv 0 \\pmod{10^9+7}$$$. Print the value of $$$P \\cdot Q^{-1}$$$ modulo $$$10^9+7$$$.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe only line of the input contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\leq n \\leq 10^{15}$$$, $$$1 \\leq k \\leq 10^4$$$).\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint a single integer — the expected value of the number on the blackboard after $$$k$$$ steps as $$$P \\cdot Q^{-1} \\pmod{10^9+7}$$$ for $$$P$$$, $$$Q$$$ defined above.\u003c/p\u003e"}},{"title":"Examples","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e6 1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e3\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e6 2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e875000008\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e60 5\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e237178099\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003eIn the first example, after one step, the number written on the blackboard is $$$1$$$, $$$2$$$, $$$3$$$ or $$$6$$$ — each occurring with equal probability. Hence, the answer is $$$\\frac{1+2+3+6}{4}\u003d3$$$.\u003c/p\u003e\u003cp\u003eIn the second example, the answer is equal to $$$1 \\cdot \\frac{9}{16}+2 \\cdot \\frac{3}{16}+3 \\cdot \\frac{3}{16}+6 \\cdot \\frac{1}{16}\u003d\\frac{15}{8}$$$.\u003c/p\u003e"}}]}