{"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 denote \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ed\u003c/i\u003e(\u003ci\u003en\u003c/i\u003e)\u003c/span\u003e as the number of divisors of a positive integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e. You are given three integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ec\u003c/i\u003e\u003c/span\u003e. Your task is to calculate the following sum:\u003c/p\u003e\u003ccenter class\u003d\"tex-equation\"\u003e\u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/1e9ab378c8acf842ab9f9b67a03afd39?v\u003d1716023834\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u003c/center\u003e\u003cp\u003eFind the sum modulo \u003cspan class\u003d\"tex-span\"\u003e1073741824\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(2\u003csup class\u003d\"upper-index\"\u003e30\u003c/sup\u003e)\u003c/span\u003e.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains three space-separated integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ec\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ea\u003c/i\u003e, \u003ci\u003eb\u003c/i\u003e, \u003ci\u003ec\u003c/i\u003e ≤ 2000\u003c/span\u003e).\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint a single integer — the required sum modulo \u003cspan class\u003d\"tex-span\"\u003e1073741824\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(2\u003csup class\u003d\"upper-index\"\u003e30\u003c/sup\u003e)\u003c/span\u003e.\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 2 2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e20\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\u003e4 4 4\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e328\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\u003e10 10 10\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e11536\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\u003eFor the first example.\u003c/p\u003e\u003cul\u003e \u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ed\u003c/i\u003e(1·1·1) \u003d \u003ci\u003ed\u003c/i\u003e(1) \u003d 1\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ed\u003c/i\u003e(1·1·2) \u003d \u003ci\u003ed\u003c/i\u003e(2) \u003d 2\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ed\u003c/i\u003e(1·2·1) \u003d \u003ci\u003ed\u003c/i\u003e(2) \u003d 2\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ed\u003c/i\u003e(1·2·2) \u003d \u003ci\u003ed\u003c/i\u003e(4) \u003d 3\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ed\u003c/i\u003e(2·1·1) \u003d \u003ci\u003ed\u003c/i\u003e(2) \u003d 2\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ed\u003c/i\u003e(2·1·2) \u003d \u003ci\u003ed\u003c/i\u003e(4) \u003d 3\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ed\u003c/i\u003e(2·2·1) \u003d \u003ci\u003ed\u003c/i\u003e(4) \u003d 3\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ed\u003c/i\u003e(2·2·2) \u003d \u003ci\u003ed\u003c/i\u003e(8) \u003d 4\u003c/span\u003e. \u003c/li\u003e\u003c/ul\u003e\u003cp\u003eSo the result is \u003cspan class\u003d\"tex-span\"\u003e1 + 2 + 2 + 3 + 2 + 3 + 3 + 4 \u003d 20\u003c/span\u003e.\u003c/p\u003e"}}]}