{"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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\" type\u003d\"text/javascript\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"panel_content\"\u003eKazari is too bored this summer holiday, she decides to play with formulas.\u003cbr\u003eFirst of all, she comes up with two positive integers $N, K$.\u003cbr\u003eShe loves power, therefore she builds a sequence $a$ where $a_i \u003d i ^ K$ $(1 \\le i \\le N)$.\u003cbr\u003eShe loves summation, therefore she calculate the partial sum of $a$ as $s$, i.e. $s_i \u003d \\sum_{j \\le i} {a_j}$ $(1 \\le i \\le N)$.\u003cbr\u003eShe also loves coprimes, therefore she calculate the sum of elements in $s$ whose index $i$ is coprime to $N$, i.e. $v \u003d \\sum_{1 \\le i \\le N, \\gcd(i, N) \u003d 1} {s_i}$\u003cbr\u003eYour task is to work out $v$. Since the answer is too large, print it modulo $998244353$.\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line of the input contains an integer $T$ denoting the number of test cases.\u003cbr\u003eEach test case starts with a positive integer $K$ $(K \\le 10 ^ 5, \\sum{K} \\le 10 ^ 6)$.\u003cbr\u003eThe second line contains a positive integer $m$ $(m \\le 20)$, indicating the number of distinct primes of $N$.\u003cbr\u003eEach of next $m$ lines contains two positive integers $p_i, a_i$ where $p_i$ is a prime $(p_i, a_i \\le 10 ^ 9, p_i \u0026lt; p_{i + 1})$.\u003cbr\u003e$$N \u003d \\prod_{i \u003d 1} ^ {m} {p_i ^ {a_i}}$$"}},{"title":"Output","value":{"format":"HTML","content":"For each test case, print an integer representing the answer modulo $998244353$."}},{"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\u003e2\r\n1\r\n2\r\n2 1\r\n3 1\r\n233\r\n1\r\n23333 1\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e16\r\n32727388\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}