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= 998244353\n\n\ndef inv_binary_unrolled(x):\n \"\"\"Unrolled version of the basic `pow` implementation\n (reference: https://x.com/torii_kyopro/status/1878460886383542626).\n \"\"\"\n res = 1\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n x = x * x % mod\n\n res = res * x % mod\n # x = x * x % mod\n\n return res\n\n\ndef inv_addition_chain(x1):\n \"\"\"Computes x^{998244351} efficiently using an optimized addition chain.\n\n The value 998244351 is represented in binary as 0b111011011111111111111111111111.\n\n This function:\n 1. Computes x^{0b1110110} using the shortest addition chain\n (reference: https://wwwhomes.uni-bielefeld.de/achim/addition_chain.html).\n 2. Calculates intermediate powers x^{0b11}, x^{0b111}, and x^{0b111111}\n (one extra operation needed to compute x^{0b111111}\n 3. Sets t = x^{0b1110110} and appends '11', '111', and '111111' x 3\n to the binary representation of the exponent\n by repeatedly squaring t and multiplying the intermediate powers.\n\n This function performs only 38 multiplication and modulo operations,\n which is improved from the 57 operations required by the basic `pow` implementation.\n \"\"\"\n\n t = x1 * x1 % mod\n x11 = t * x1 % mod\n t = x11 * x11 % mod\n x111 = t * x1 % mod\n t = x111 * x111 % mod\n t = t * t % mod\n t = t * t % mod\n x111111 = t * x111 % mod\n t = t * x11 % mod\n t = t * t % mod\n\n # t = x1110110\n\n t = t * t % mod\n t = t * t % mod\n t = t * x11 % mod\n\n t = t * t % mod\n t = t * t % mod\n t = t * t % mod\n t = t * x111 % mod\n\n t = t * t % mod\n t = t * t % mod\n t = t * t % mod\n t = t * t % mod\n t = t * t % mod\n t = t * t % mod\n t = t * x111111 % mod\n\n t = t * t % mod\n t = t * t % mod\n t = t * t % mod\n t = t * t % mod\n t = t * t % mod\n t = t * t % mod\n t = t * x111111 % mod\n\n t = t * t % mod\n t = t * t % mod\n t = t * t % mod\n t = t * t % mod\n t = t * t % mod\n t = t * t % mod\n t = t * x111111 % mod\n\n return t\n\n\n# Both blocks have a runtime of approximately 1000 ms.\n\nres = 0\nfor i in range(1, 10**7):\n res += inv_binary_unrolled(i)\nprint(res)\n\nres = 0\nfor i in range(1, 10**7):\n res += inv_addition_chain(i)\nprint(res)\n","codes",[],"stdin","compiler","createdAt",1736745261,"title","description","isPrivate","compilerInfo",{"_11":1644,"_13":1645,"_15":1315,"_17":1646,"_19":3461,"_22":25,"_24":23,"_26":1648,"_28":3462},[1646],[],"results",[3465,3469,3472,3475],{"_31":3466,"_3467":3468},"Control","data","Start",{"_31":3470,"_3467":3471},"StdOut","4995507776284649\n4995507776284649\n",{"_31":3473,"_3467":3474},"ExitCode","0",{"_31":3466,"_3467":3476},"Finish","hpplib",[3479,3496,3507,3518,3527,3536,3545,3554,3564,3575,3586,3597,3608,3619,3630,3641],{"_11":3480,"_3481":3482,"_3457":3483,"_3484":3485,"_3486":3487,"_3492":3493},"CLI11","repository","CLIUtils/CLI11","CLI11 is a command line parser for C++11 and beyond that provides a rich feature set with a simple and intuitive interface.","headerDescription","","wandbox",{"_3488":3489,"_3490":3491},"tagName","v2.7.2","publishedAt","2026-08-02T14:12:37Z","clangd",{"_3488":3494,"_3490":3495},"v2.5.0","2025-02-27T12:29:12Z",{"_11":3497,"_3481":3498,"_3457":3499,"_3484":3500,"_3486":3501,"_3492":3504},"cxxopts","jarro2783/cxxopts","Lightweight C++ command line option parser","",{"_3488":3502,"_3490":3503},"v3.3.1","2025-05-26T08:12:04Z",{"_3488":3505,"_3490":3506},"v3.2.0","2024-02-15T05:32:43Z",{"_11":3508,"_3481":3509,"_3457":3510,"_3484":3511,"_3486":3512,"_3492":3515},"nanobench","martinus/nanobench","Simple, fast, accurate single-header microbenchmarking functionality for C++11/14/17/20","",{"_3488":3513,"_3490":3514},"v4.6.0","2026-08-14T14:26:30Z",{"_3488":3516,"_3490":3517},"v4.3.11","2023-02-16T19:06:26Z",{"_11":3519,"_3481":3520,"_3457":3521,"_3484":3522,"_3486":3523,"_3492":3526},"toml11","ToruNiina/toml11","TOML for Modern C++","",{"_3488":3524,"_3490":3525},"v4.4.0","2025-02-15T16:20:52Z",{"_3488":3524,"_3490":3525},{"_11":3528,"_3481":3529,"_3457":3530,"_3484":3531,"_3486":3532,"_3492":3535},"toml++","marzer/tomlplusplus","Header-only TOML config file parser and serializer for C++17.","",{"_3488":3533,"_3490":3534},"v3.4.0","2023-10-13T13:45:17Z",{"_3488":3533,"_3490":3534},{"_11":3537,"_3481":3538,"_3457":3539,"_3484":3540,"_3486":3541,"_3492":3544},"rapidjson","Tencent/rapidjson","A fast JSON parser/generator for C++ with both SAX/DOM style API","",{"_3488":3542,"_3490":3543},"v1.1.0","2016-08-25T08:01:22Z",{"_3488":3542,"_3490":3543},{"_11":3546,"_3481":3547,"_3457":3548,"_3484":3549,"_3486":3550,"_3492":3553},"picojson","kazuho/picojson","a header-file-only, JSON parser serializer in C++","",{"_3488":3551,"_3490":3552},"v1.3.0","2015-02-25T04:12:53Z",{"_3488":3551,"_3490":3552},{"_11":3555,"_3481":3555,"_3457":3556,"_3484":3557,"_3486":3558,"_3492":3561},"nlohmann/json","JSON for Modern C++","",{"_3488":3559,"_3490":3560},"v3.12.0","2025-04-11T08:43:39Z",{"_3488":3562,"_3490":3563},"v3.11.3","2023-11-28T21:38:09Z",{"_11":3565,"_3481":3566,"_3457":3567,"_3484":3568,"_3486":3569,"_3492":3572},"csv-parser","vincentlaucsb/csv-parser","A modern C++ CSV parser and serializer that doesn't make you choose between ease of use or performance.","",{"_3488":3570,"_3490":3571},"v5.8.0","2026-11-12T04:24:01Z",{"_3488":3573,"_3490":3574},"2.3.0","2024-06-15T20:23:18Z",{"_11":3576,"_3481":3577,"_3457":3578,"_3484":3579,"_3486":3580,"_3492":3583},"rapidcsv","d99kris/rapidcsv","C++ CSV parser library","",{"_3488":3581,"_3490":3582},"v9.07","2026-08-15T06:49:41Z",{"_3488":3584,"_3490":3585},"v8.84","2024-09-28T05:31:16Z",{"_11":3587,"_3481":3588,"_3457":3589,"_3484":3590,"_3486":3591,"_3492":3594},"fmt","fmtlib/fmt","A modern formatting library","",{"_3488":3592,"_3490":3593},"12.2.1","2026-11-07T16:45:44Z",{"_3488":3595,"_3490":3596},"11.1.4","2025-02-26T18:33:33Z",{"_11":3598,"_3481":3599,"_3457":3600,"_3484":3601,"_3486":3602,"_3492":3605},"NumCpp","dpilger26/NumCpp","C++ implementation of the Python Numpy library","",{"_3488":3603,"_3490":3604},"Version_2.17.0","2026-09-24T02:22:33Z",{"_3488":3606,"_3490":3607},"Version_2.14.0","2025-02-09T04:16:30Z",{"_11":3609,"_3481":3610,"_3457":3611,"_3484":3612,"_3486":3613,"_3492":3616},"spdlog","gabime/spdlog","Fast C++ logging library.","",{"_3488":3614,"_3490":3615},"v1.17.0","2026-01-04T16:51:07Z",{"_3488":3617,"_3490":3618},"v1.15.1","2025-02-01T12:08:58Z",{"_11":3620,"_3481":3621,"_3457":3622,"_3484":3623,"_3486":3624,"_3492":3627},"expected-lite","martinmoene/expected-lite","expected lite - C++23 expected objects for C++11 and later in a single-file header-only library","",{"_3488":3625,"_3490":3626},"v0.10.0","2025-11-17T22:35:10Z",{"_3488":3628,"_3490":3629},"v0.8.0","2024-06-05T21:24:45Z",{"_11":3631,"_3481":3632,"_3457":3633,"_3484":3634,"_3486":3635,"_3492":3638},"gsl-lite","gsl-lite/gsl-lite","ISO C++ Core Guidelines Library implementation for C++98, C++11 up","",{"_3488":3636,"_3490":3637},"v1.1.1","2026-08-20T06:59:25Z",{"_3488":3639,"_3490":3640},"v0.42.0","2024-11-01T20:24:11Z",{"_11":3642,"_3481":3643,"_3457":3644,"_3484":3645,"_3486":3646,"_3492":3649},"ut","boost-ext/ut","C++20 μ(micro)/Unit Testing framework","",{"_3488":3647,"_3490":3648},"v2.3.1","2025-04-02T13:02:52Z",{"_3488":3650,"_3490":3651},"v2.3.0","2025-02-04T11:58:39Z","env",{"_3654":3655,"_3656":3657,"_3658":3659,"_3660":3661,"_3662":3663,"_3664":3665,"_3666":3667,"_3668":3669,"_3670":3671},"KV_CACHE",{},"KV_SESSION",{},"R2_BUCKET",{},"WANDBOX_GITHUB_CLIENT_ID","f9d429d939d997e6b08e","WANDBOX_GITHUB_CLIENT_SECRET","d99b3d12225671cde514d9e2b3d5cc8356f4ed5f","WANDBOX_KV_COOKIE_SECRET","FaCnykHoYzqiXReGkgvmcYGvQdQ4yZUE","WANDBOX_R2_PREFIX","master/","WANDBOX_URL_PREFIX","https://api.wandbox.org","ASSETS",{},"root","actionData","errors"]