{"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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eLet\u0027s call an array $$$[a_1, a_2, \\ldots, a_k]$$$ of positive integers \u003cspan class\u003d\"tex-font-style-bf\"\u003ephenomenal\u003c/span\u003e, if the product of its elements is equal to the sum of its elements (i.e. if $$$a_1 a_2 \\ldots a_k \u003d a_1 + a_2 + \\ldots + a_k$$$) .\u003c/p\u003e\u003cp\u003eFor example, the array $$$[2, 2]$$$ is phenomenal, because $$$2\\cdot 2 \u003d 2+2 \u003d 4$$$, and $$$[3, 1, 2]$$$ is phenomenal, because $$$3\\cdot 1 \\cdot 2 \u003d 3 + 1 + 2 \u003d 6$$$, but the array $$$[2, 3]$$$ is not phenomenal, as $$$2\\cdot 3 \\neq 2+3$$$.\u003c/p\u003e\u003cp\u003eLet $$$f(i)$$$ denote the number of phenomenal arrays of size $$$i$$$. It can be shown that for any fixed $$$i \\ge 2$$$ there is only a finite number of phenomenal arrays of size $$$i$$$.\u003c/p\u003e\u003cp\u003eYou are given an integer $$$n$$$. Find $$$f(2), f(3), \\ldots, f(n)$$$. As these numbers can be very big, output them modulo $$$P$$$, where $$$P$$$ is a given prime number.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe only line of the input contains two integers $$$n, P$$$ ($$$2 \\le n \\le 2\\cdot 10^5$$$, $$$10^8 \\le P \\le 10^9$$$, $$$P$$$ is prime).\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eOutput $$$n-1$$$ integers\u0026nbsp;— the values $$$f(2), f(3), \\ldots, f(n)$$$ modulo $$$P$$$.\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\u003e7 804437957\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1 6 12 40 30 84 \n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}