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For people looking for maximum performance, they should use something like gmpy2.Nneed_hiFshowcL\4p\4pV0pV'dVP4pW9gW8:dK&VPV4V^, pW, p V'dT MTp VPV 4VPV 4W8wgK~VPW , 4KVP4p \4p V 'dj\ V 4pV P V4V^, pW8gK5V^, V 9gKEW9gKMV PV4V PV4KqV'g V 'dQh/p \ Wl,4FpV^, pW, p V^, V 9d-V'd\RRR7W^, ,V,pMW9dfV'd\RRR7W,W,,pW8wd5V'd\RRR7^V,^,V8XgQhW,pMV'd\RRR7W,pV'd\RYV9dRMR 4WV&K WmP48:gQhV P4V, ;p'dV'gQhVFpWK V #) z* base)endsquarez * basepowz atneededextra) setpopaddcopymaxremovesortedprintkeys)wbase more_thanrrseenneedwslohiwhichcandsr dnresultexcesss&&&$$ -D:/M/msys64/mingw64/lib/python3.14/_pylong.pycompute_powersr$9s 5D 5D B FFH 9   !V V2  u 8 FF19  IIKE EE  J Q !V >ac.2? IIbM IIbM %  A DL ! !V V Q3!8hB'sVd]F WhB'UQU]Fx),2vzQ&e$YF  %T Hw ?!1"4 668  D v wA Hc8aaaa^RIHo^oVVVV3Rlo\P!\4;_uu_4VP 4p\ VS!^4S4oV^8dRpV)pMRpS!W4pV'dV)pRRR4V# +'giX#;i)z6Asymptotically fast conversion of an 'int' to Decimal.)Decimalc<VS8:d S!V4#V^, pW, pV^V,^, ,pS!WB4S!W1V, 4SV,,,#r) r rw2rrBITLIMDinnerw2pows && r#r.int_to_decimal..innersV ;Q4K !V W 17a- R}uRR059<<.innersQ ;q6M !V59%RR 5=#6#6r#:::r%gyPD?-r0)r4_decimalr:r7intr$itemslstrip) r rkvsignsr=r.r>s & @@@r#int_to_decimal_stringrJs A7{x+>!$%%F; A" "Q &'A 1a (E 6a1u B a Ats{q HHSM 8Or%cpaaaaRoVVVV3Rlo\\S4^S4oS!^\S44#)z6Asymptotically fast conversion of a 'str' to an 'int'.ic<W, S8:d\SW4#W,^,^, pS!W!4S!W4SW, ,,W, ,,#r))rC)abmidr=r.rIw5pows&& r#r. _str_to_int_inner..innersW 5F?qv; uqyQc !ME!'N2!" #r%)r$len)rIr=r.rPsf@@@r#_str_to_int_innerrSs9F## 3q61f -E CF r%z0x1.a934f0979a371p-2) defaultdictGUARDc xaa a a aaRo \Pp\4oS^8gQhV VV V VV3Rlo VP4pV\,p\ V4pV^,WE, R8,pVP 4^.8d\RV R24h\P!\4;_uu_4o V!R4p\WgS RR7o\V^V, S RR7p^S P\P&\PS nSP4F6wrV P!4S,^,S nWV ,53SV &K8 ?\P$S nS !V!V4V4RRR4\ P'S4# +'giL%;i) ic<VS 8:d5SP\\V44PV44R#V^, pW, pST,wrg\ TP 4TP 4, ^4S ,S nT5T5,p\PS nTP4pYT,, pT^8gQh^pYV8d1^pYV,pT^, pYV8dRp\ YV4wrYI, p\T;;,^, uu&S !YB4?S !YS4R#)Ni) extendrCr:to_bytesr;radjustedprecr1MAX_PRECto_integral_value_spread)r rw1r+rrp256recipcounthi2BYTELIMrUctxr.pow256r!s&& r#r.$_dec_str_to_int_inner..inners < MM#c!f+..q1 2  !V V !*KD 1::<$--/91=ECHufB''CH%%'B$YB7N7Ez a:  E$R.GCIB ENa N b  b r%g?zcannot convert string of len z to intT)rN)r1r' bytearray__len___LOG_10_BASE_256rCr4 ValueErrorr2r3r$trapsInexact ROUND_DOWNroundingrDrZr[r\ from_bytes)rIrUr-lenSlog_ub log_ub_as_intrD256rpow256rFrGrdrer.rfr!s&d @@@@@r#_dec_str_to_int_innerrwsh GA [F 19977L 99;D $ $FKMV3c9:A  ||~8gFGG   4 5 5v$? AHgtD &' '//")) LLNDA zz|e+a/CHAJ;F1I# ## adA- 6. >>& !!/ 6 5s >CF)) F9 cVP4PRR4p\p\V4R8d\e\ pV!V4#)zkAsymptotically fast version of PyLong_FromString(), conversion of a string of decimal digits into an 'int'._ri)rstripreplacerSrRrBrw)rIfuncs& r#int_from_stringr}s@  3#A D 1vx3$ 7Nr%c\P!RV4pV'g \R4h\VP ^44pVP ^4R8XdV)pV#)zBAsymptotically fast version of decimal string to 'int' conversion.z\s*([+-]?)([0-9_]+)\s*z&invalid literal for int() with base 10r@)rematchrlr}group)rImrGs& r# str_to_intrsR *A.A ABB #AwwqzS B Hr%icVP4V, \8:d \W4#V^,pV'dV^,pV^,pV^, pV^, p^V,^, pW, W,rv\W, W, V,WWt4wr\WV,WWt4wrV'd V ^,p W,V ,V 3#)a2Divide a 2n-bit nonnegative integer a by an n-bit positive integer b, using a recursive divide-and-conquer algorithm. Inputs: n is a positive integer b is a positive integer with exactly n bits a is a nonnegative integer such that a < 2**n * b Output: (q, r) such that a = b*q+r and 0 <= r < b. )r4 _DIV_LIMITr;_div3n2n) rMrNr padhalf_nmaskb1b2q1rq2s &&& r#_div2n1nrs ||~Z'a| a%C  a a Q !VF K1 D [!( QVakT11" EEB QD! 4EB  a <" a r%cW, V8Xd'^V,^, WV,, V,rvM\WV4wrgWu,V,Wd,, pV^8dV^,pWr, pKWg3#)zAHelper function for _div2n1n; not intended to be called directly.)r)a12a3rNrrr qrs&&&&&& r#rrsc x2~Q!|S!G_r11# "A a% Q  4Kr%caaa^.VP4S,^, S,,oVVV3RloV'dS!V^\S44S#)a2Decompose non-negative int a into base 2**n Input: a is a non-negative integer Output: List of the digits of a in base 2**n in little-endian order, meaning the most significant digit is last. The most significant digit is guaranteed to be non-zero. If a is 0 then the output is an empty list. c<V^,V8XdVSV&R#W,^, pW1, S ,pW, pWV,, pS!WaV4S!WSV4R#)rNr*) xLRrOshiftupperlowera_digitsr.r s &&& r#r._int2digits..innersW q5A:HQK ulA  e^$ e e!r%)r4rR)rMr rr.s&f@@r# _int2digitsrsEsq||~)A-!34H   aCM" Or%cPaaaVVV3RloS'dS!^\S44#^#)zxCombine base-2**n digits into an int. This function is the inverse of `_int2digits`. For more details, see _int2digits. c<V^,V8Xd SV,#W,^, pW , S,pS!W!4V,S!W4,#r)r*)rrrOrdigitsr.r s&& r#r._digits2int..innersF q5A:!9 ulA c &%-77r%)rR)rr r.sff@r# _digits2intrs" 8%+5CK 11r%cVP4p\W4p^p.p\V4F/p\WB,V,W4wrtVP V4K1 VP 4\ WR4pW3#)zWDivide a non-negative integer a by a positive integer b, giving quotient and remainder.)r4rreversedrappendreverser) rMrNr rrq_digitsa_digitq_digitrs && r# _divmod_posrsr A1 H AHH%qv0!7  & H A 4Kr%cV^8Xd \R4hV^8d\V)V)4wr#W#)3#V^8d\V(V4wr#V(W(,3#\W4#)zyAsymptotically fast replacement for divmod, for 'int'. Its time complexity is O(n**1.58), where n = #bits(a) + #bits(b). zdivision by zero)ZeroDivisionError int_divmodr)rMrNrrs&& r#rrsk Av 233 Q1"qb!"u Q1"a r1r6z1  r%),__doc__rr1rB ImportErrorr$ getcontextrr3r\r[MAX_EMAXEmaxMIN_EMINEminrmrnr7rJrSfloatfromhexrk collectionsrTrCr^rwr}rrrrrrrrconsumer itertoolschainrlimitrangerr*r%r#rs > NJ %J eJ X!++-224%..%..%..01W__-%N+ZJ==!78$ c t"at"l   "  < > 2" !b]HsC CC