{"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\"\u003e有三个集合 $S_1$, $S_2$, $S_3$,每个集合都是 {1, 2, ...., $n$} 的子集,现有如下条件。\u003cbr\u003e|$S_1$| + |$S_2$| + |$S_3$| \u003d $k$\u003cbr\u003e|$S_1$| ≥ $a_1$, |$S_2$| ≥ $a_2$, |$S_3$| ≥ $a_3$\u003cbr\u003e|$S_1$ ∪ $S_2$| ≥ $a_4$, |$S_2$ ∪ $S_3$| ≥ $a_5$, |$S_1$ ∪ $S_3$| ≥ $a_6$\u003cbr\u003e|$S_1$ ∪ $S_2$ ∪ $S_3$| ≥ $a_7$\u003cbr\u003e求有多少种集合 ($S_1$, $S_2$, $S_3$) 的有序三元组满足上述要求,请输出答案模 1, 000, 000, 007。\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"第一行输入两个整数 $n$, $k$。\u003cbr\u003e第二行输入7个整数 $a_1$, $a_2$..., $a_7$。\u003cbr\u003e1 ≤ $n$ ≤ 1, 000, 000\u003cbr\u003e1 ≤ $k$ ≤ 50\u003cbr\u003e0 ≤ $a_i$ ≤ 3"}},{"title":"Output","value":{"format":"HTML","content":"一行一个整数表示答案。"}},{"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\u003e4 4\r\n1 1 1 2 2 2 3\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e180\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}