{"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\"\u003eWe will give you a non-negative integer $m$ and a prime number $p$. \u003cbr\u003eAnd we define $f\\left(i\\right)$ is the number of pair$\\left(x,y\\right)$ that satisfies $\\left(x + y\\right) ^ {i} \\equiv x ^ {i} \\% p$ and $1 \\leq x \\leq p - 1,1 \\leq y \\leq m$.\u003cbr\u003eNow, you have to calculate the sum $\\sum_{i\u003d1}^{p-1}if\\left(i\\right)$. \u003cbr\u003eMaybe the sum is too big,so you only need to output the sum after mod $1e9+7$.\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line contains only one integer $T$, which indicates the number of test cases. \u003cbr\u003eFor each test case, there are a integer $m \\left(1 \\leq m \\leq p - 1 \\right)$ and a prime number $p\\left(2 \\leq p \\leq 1e9 + 7 \\right)$ on one line. \u003cbr\u003e"}},{"title":"Output","value":{"format":"HTML","content":"For each test case, output one line \"Case #x: y\", where x is the case number (starting from 1) and y is the sum after mod $1e9+7$."}},{"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\u003e3\r\n5 7\r\n3 11\r\n2 103\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eCase #1: 210\r\nCase #2: 390\r\nCase #3: 50388\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}