{"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\u003eThe Little Elephant is playing with the Cartesian coordinates\u0027 system. Most of all he likes playing with integer points. The Little Elephant defines an integer point as a pair of integers \u003cspan class\u003d\"tex-span\"\u003e(\u003ci\u003ex\u003c/i\u003e;\u0026nbsp;\u003ci\u003ey\u003c/i\u003e)\u003c/span\u003e, such that \u003cspan class\u003d\"tex-span\"\u003e0 ≤ \u003ci\u003ex\u003c/i\u003e ≤ \u003ci\u003ew\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e0 ≤ \u003ci\u003ey\u003c/i\u003e ≤ \u003ci\u003eh\u003c/i\u003e\u003c/span\u003e. Thus, the Little Elephant knows only \u003cspan class\u003d\"tex-span\"\u003e(\u003ci\u003ew\u003c/i\u003e + 1)·(\u003ci\u003eh\u003c/i\u003e + 1)\u003c/span\u003e distinct integer points.\u003c/p\u003e\u003cp\u003eThe Little Elephant wants to paint a triangle with vertexes at integer points, the triangle\u0027s area must be a positive integer. For that, he needs to find the number of groups of three points that form such triangle. At that, the order of points in a group matters, that is, the group of three points \u003cspan class\u003d\"tex-span\"\u003e(0;0)\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e(0;2)\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e(2;2)\u003c/span\u003e isn\u0027t equal to the group \u003cspan class\u003d\"tex-span\"\u003e(0;2)\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e(0;0)\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e(2;2)\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eHelp the Little Elephant to find the number of groups of three integer points that form a nondegenerate triangle with integer area.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eA single line contains two integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ew\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eh\u003c/i\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(1 ≤ \u003ci\u003ew\u003c/i\u003e, \u003ci\u003eh\u003c/i\u003e ≤ 4000)\u003c/span\u003e.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eIn a single output line print an integer — the remainder of dividing the answer to the problem by \u003cspan class\u003d\"tex-span\"\u003e1000000007\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e + 7)\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 1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e36\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\u003e2 2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e240\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}