{"trustable":false,"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":"Problem Statement","value":{"format":"HTML","content":"\u003cp\u003eYou\u0027re given two \u003ci\u003edigits\u003c/i\u003e $a$ and $b$.\u003c/p\u003e\n\n\u003cp\u003eA positive integer is \u003ci\u003egood\u003c/i\u003e, if its decimal representation consists of only $a$ and $b$.\u003c/p\u003e\n\n\u003cp\u003eA \u003ci\u003egood\u003c/i\u003e positive integer is \u003ci\u003eexcellent\u003c/i\u003e, if the sum of its digits is also good.\u003c/p\u003e\n\nFind out the number of excellent numbers of length exactly $n$ (i.e. consists of $n$ digits), modulo $10^9 + 7$."}},{"title":"Constraints","value":{"format":"HTML","content":"\u003cul\u003e\n\u003cli\u003e$1 \\le a \u003c b \\le 9$\u003c/li\u003e\n\u003cli\u003e$1 \\le n \\le 10^6$\u003c/li\u003e\n\u003c/ul\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe only line of the input contains three integers: $a, b$, and $n$."}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint a single integer — the answer to the problem modulo $10^9 + 7$."}},{"title":"Sample 1","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 3 3\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Sample 2","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 3 10\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e165\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}