Problem:
Score : 500 points

Problem Statement

For integers b (b \geq 2) and n (n \geq 1), let the function f(b,n) be defined as follows:

f(b,n) = n, when n < b

f(b,n) = f(b,\,{\rm floor}(n / b)) + (n \ {\rm mod} \ b), when n \geq b

Here, {\rm floor}(n / b) denotes the largest integer not exceeding n / b,
and n \ {\rm mod} \ b denotes the remainder of n divided by b.

Less formally, f(b,n) is equal to the sum of the digits of n written in base b.
For example, the following hold:

f(10,\,87654)=8+7+6+5+4=30

f(100,\,87654)=8+76+54=138

You are given integers n and s.
Determine if there exists an integer b (b \geq 2) such that f(b,n)=s.
If the answer is positive, also find the smallest such b.

Constraints

1 \leq n \leq 10^{11}

1 \leq s \leq 10^{11}

n,\,s are integers.

Input

The input is given from Standard Input in the following format:

n
s

Output

If there exists an integer b (b \geq 2) such that f(b,n)=s, print the smallest such b.
If such b does not exist, print -1 instead.

Sample Input 1

87654
30

Sample Output 1

10

Sample Input 2

87654
138

Sample Output 2

100

Sample Input 3

87654
45678

Sample Output 3

-1

Sample Input 4

31415926535
1

Sample Output 4

31415926535

Sample Input 5

1
31415926535

Sample Output 5

-1

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use num_integer::sqrt;
use contest::scanner::Scanner;
use std::cmp::min;

fn main() {
    let mut scan = Scanner::new();
    let n = scan.read::<i64>();
    let s = scan.read::<i64>();
    if n < s {
        println!("{}", -1);
        return;
    }
    if n == s {
        println!("{}", n+1);
        return;
    }
    let sqrt_n = sqrt(n);
    for b in 2..=sqrt_n {
        if calc(n, b) == s {
            println!("{}", b);
            return;
        }
    }
    let mut ret = 1i64<<60;
    for p in 1..sqrt_n {
        let b = (n - s) / p + 1;
        if b != 1 && calc(n, b) == s {
            ret = min(ret, b);
        }
    }
    println!("{}", if ret == 1i64<<60 {-1} else {ret});
}

fn calc(mut n: i64, b: i64) -> i64 {
    let mut ret = 0;
    while n > 0 {
        ret += n % b;
        n /= b;
    }
    ret
}
*/

fn main() {
    let exe = "/tmp/binD1FDFDC9";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &[u8]) -> Vec<u8> {
    let mut tbl = [0; 256];
    for i in 0..85 { tbl[TBL[i] as usize] = i as u32; }
    let mut v_vec = v.to_vec();
    let padding = (5 - v.len() % 5) % 5;
    v_vec.extend(vec![b'~'; padding]);
    let mut ret = vec![0u8;v_vec.len() / 5 * 4];
    for (i, ck) in v_vec.chunks(5).enumerate() {
        let mut acc = 0;
        for &c in ck {
            acc = acc * 85 + tbl[c as usize];
        }
        ret[i * 4..(i + 1) * 4].copy_from_slice(&unsafe{std::mem::transmute::<u32, [u8; 4]>(acc.to_be())});
    }
    let l = ret.len();
    ret.resize(l - padding, 0u8);
    ret
}

const TBL: &'static [u8] = b"0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz!#$%&()*+-;<=>?@^_`{|}~";
const BIN: &'static [u8] = b"e??420s#R400000000000suY$0RR91P^>`!00000KmY&$00000000000000000000Kma%Z0{}n(000000RR911poj50000000000002M$00000002M$00000m$d-^00000m$d-^00000001BW000000RR911^@s600000000000Kh>2000000Kh>2000000000000000sN5j{0000001yBG00000QRQ@G1^@s6000000000000000000000000000000000000000000000000005C8xG00000+&hJ7RZv(VR0$0h00000poIefpoIefkO2SymH+?%0ssI2`}-mPe??420s#R40suY$4G;rB4;%7r76ky{fdc>&fgQVhH~<C(4*(7;1pojoAy3#q2T)%F0Nd>Q&L99c1`THy2V=rMJ0Un4Er>M$H^Bz7ZU+MdH!v;acbBlpHGk!FWH;;<gghbJ2SdyW019j~*aSCG1^@sE3wH7l08($KU<e8O;1~c0fdBvi0001x0RO;U0|5J@0RRF?4FLcD2l7x@!vH~7K~^!qK~+IiNrTM)RZ~f~xBvf%{!EF_PK_)ANQ3N1NQpEg156|c6X8so`)_v#DDtijR3sQki<BgQJrno-kGyRU$PJ7nh(shHNcYf6jT|8V+uPqk94k$YdjS(%BoGAt=nVmryhw$>TKhHkbbd^WKm;m@$2wr|xpvnJSV;lJ2P#=h+O~ab8xM)m^P~j95_EvJwQc(e&I0cj*$NS~ezyB=J4lT=JVipr1Q-BeV*EpH8|>MHK8uW?`XBD5Z~wRNL5akI{ME!rM2X;AT|rzy171O2&Bu2C!&OX;4OZ;}Obs6f6+j3BHCw~)+oJ3ZLAY=MjO9}f2owdqZH4Y+Wg}b|G85lW0&Y=u-|e0UZ5#wrJ|q~4d?XAEQw9CmUHb$EC<e1Aixj1WNHOj9c6+xm=UwCczyB`e@D%_7l3e!g?RHlKi#Lr0{;`IO4dHugg?H}uMKQ@2J%`CXQIckmt=qQk{!>tZKLT?I$Ov1&!%h42clX=-_6SLfJ_1Gv{}2TmcnAP=2@~%=?0f$eb9}ISFaITC5N0k9ACkRcgoOW46<o{@3lC$rBkXS2y9S|TD83PT01J&7-!wcTL@z51fm}E|!tD5f1)BpO%`m=wb8|N+0KW|cbWVGN`2P=t`P{<44+TOGSHKSum%thauw;-y2B46D?DKqENpJ*UP(a5z!q^Y(1Ok97S^;l3C>slf_BA1Cs3As;I5-9DKgPccHQq7OLI2jj2Ml|TjrM*iFj~iR<2l?m+D1?iHWl`%Tzc;7{<iiP7y@)vz5pG+AiC3R2KVUzxgs98{{V$4LcQ*r%+tk!5KtH|u5+84Sv`q-Sylxsgxej4O!WFa>3s{o1Q-2dC3oI=Lj*!x#{g|%X>Rbv%8$zrC<PO+?n5|x*k0Ol&&-R*4-ow57byq*y0>P~WPv;-D3Sw11lvP%kG&6z1SNuvfFKqQ=<bi^ZNUL!$q$Zg2?7s=3SzVNzKo<eDr`$_fDGBzpKVZ8>t6e|$(Sifs34E6hh^*$O@liCSf&Fcw$N}3RbzW-Nfa+{cl-83An*$)0d)yMdmzlzTtm{<wZkAuHGc#_eFXXRc-z{E93}&<jU5E0;e2PIN+OF0V&jcFws(VK2Ba{kUi^vgv+)b>iv^G?i34?FiP(t59d;+vTh7dC&HQ2YV9(x}1KaB&4~fGP1TpY8X5Y5vFO~{XP?zt=(8gQuNd19wX`BeYM)WpZZh2F@#;e3II3w+T5SIZ`T<eH5Cf6hcM<~ylcSkSRT<E?59NU#=5CRM;-^^ceZDYG7hZr7k)=7fKc1xOeCK+$9I9NHEkVz2gncbGO<R{z*096+va5}KA6=%eH;QcxXUL$xH1>6s?eQ0Qw9#8@O3!fDz<L+hKyhQ*Gj|ZFS6TiO*zYSfJ93FQIc^IF27iby2bWq0_x@5+`9hclr1}OD*j>o#mJ+(+32ODWblNhkE2Qa@VSH>>XHf@Y$t}#F<5n4bXpyP8hv@J4VM+mWX@aQoMj*=sTY}ek_z>OJ2K%EF<v(3QR9SYz33sDwnn$B$qP-Q(36DWfL8M`aLNPtD<d*63wlaQjUIam<JKo~eEy|M8(D~UxJiA@|4eYwX)DCYay_ts{cU<DCHFvdkdC?E{NUzQ_5L`8)5bSh4cw+T5QNz`>H0tHdQZSENGJt77lWROd3Eg%P}btmm$SC~CLifGSpe=U93(H%AocnTcv2n}q&UkLW~3V_>5DZ_myjoiK4K1^{iNDpqn3mCQn$n6bVw>@kFf3y(n2|;xZuWw%yrNflD2oEcK+YgAh!m~H_Nw@$25KZYL`vm*;ZQT!o9~fT2M#Dm41$?Vhx!;Yw4_pO=2Pjq*$np<Z$fLcDeY*xx!2=Kt>8u*i3tZ9i+xNk~H!Q+Qx>kTpG0+j{9xkwrZMVS(L+E+!_H>Nci!Zh)%Ubm^0R$V&@omupIq!BJ-x&85z1wbO_%Dh57{?@X=j$KIx*@y<`0E-tLB&K{VC>%k=qowJcj3qVA&tiz{&l;vO*st5z{^PwMaE>X;q@GF1hp?9Y?#42X6p6@oLwXK1O|f<RssY-G%ND!-Yy$Z5?BGiYXT2EPz(lO8-xq3Z5Uvn6ig2Z%XFuO4ocKAXz{;OySgG<*of9$zuSH=F_7L=xn|vuB6R!K?8oUq51g(6&Z)3%FZ<;GBuJU?`5V`*84lkEfAdT^&kWHsC-&Hd{qcOl>oK@fko8T4$tQQA?P7g7=v<2d!3YkAup#Pv-!Y8&*Tw!8G1Djt@V@1wS|70+2W;yXe}l$JIqpt}ukS+jiP(?+aOTRf+dI~S$8!u2wR0apuQ&R^w*PL?ugP`3NjZ@ZPj_>L?f2`oJ;%?Q4Mq1Jh3rQ+21NINIrUr}ecQlsi*N%u_kYpO>jrKa@618Fon@j0Tchpx`~P(u-3%%U>tpNKHuh#j7m+Gx+X#YuFWW>{&`J0Ew9^K=Z2RdQ1pmDDxYiDPYe(w>5P!~fqr94^IRcy5A;qo&XBi=bNK01bF+BzwrXKPJV30k?&hAhUxHrBd`G*0Kz3f;;z6dnGC=fZe3&}`HgR+5uYvxI}q$(Me=33-AnUFc#<R1cdP9~ws&(bhDFrYv$3VPv&<BLa{MJe&H(GP>vYhmk^I}Y<N(?XYSo1uTFN(@dp+4e`-VMC)2Y9UR%W^^%s?LwhKR>=(#ac8~_FKi~nm*jPFxD7`gLk3QE49kab8dvKWtW=B^S$b#x=;pRk^C4Y4RCP>dbIo0oBqSy`RTWnuCkNQ;B`+-;2vXa|6Eh}ZUPT4r8MABiiQiu^i5K<;9R5TAf2jhm3|>H>tX2%(R}%<1<5=ukV=40pE_FZ*Y-4q=4|O=kNd!nZAa?K=Z3J`?6C8?LJOb{~8$WdpYvW`jBFZ1~R(NwW2`y{EkOn;|!q_0d?duzTfB>Q1JaB_{><_j*bZZDEAxR1geRZP_F>Z<w0RJCpBw9R;5h{&M_kj5Ya>GD?e*u2`{UCI`Krh8Wgzb5+!brjD2146D+-?svD$V`|#t~ge6k-LQ`+g6j!g7?h0XP@D1$cdZzX8w)^Vl0N6=-TWy>upu7PW8S?b`veDEljP2Lvs3K9qy`0d&6I;701wbVrR>Gy(bRFI>6s;UfkHi?MHio(9v0zY%b2gLqxSw-y8%Efo4O+h%Xv*0v*EbW)%)1kgb%b^G6>33s_jYugHNvo*p2@GOnp4uA7;-0P;gfHDssFCyngKG)C}FfEIPDKDdUYz?g~-fIr1G3`M{ID7{Vtq-#qhGv@sHu0Gp5VfY@J0TWfS6X!x(`3{F{~|UTxIl<3FcJ<cgg1#1+|qzNcIg^y>nb=zh%~c-5R2K=HNPzqwnPnd*%7wJJRo;1#At7zxd1+#z`DT!+eJHr$*OoI#k*yP!H2rK2*v#muMT94PsqXP2q_HzOAmHU54Y$r-ihnM>js16KPN(V?7`&-KDq)@UiV+{7#WRG0$Pof9l(GiA>VJf`@HjJi4+KP!33Di7<_Z!TPtiIfXTp!Qy`>x1I;7M9EE^%@7R|DwwAIbezpW4-6X!lbci5k$_Z|Aq;@@6`DVtKU{%2FgnUrGD~Mnhx&|D9V}lWl67;|;u3?9)1JWyy!!J<(AsZ6>7cszD!)A{Ufdv>?PEOZE=sGrpvW;$EMgxA}z5w4fIrw!4h!6sDK?~NbZu=P$su)w~OKcG80FONZIqd%P4{y!k@HbxlbvpANe?|yN#|HQS8x_E{68fa6yt$SPk*onrQh^}14ZTU}O8<Vxq}D^<wuPr4v_5tJeK-$rz)ogjzZbSi8N{YMBuQ=m5C*~08w;Qc7T?iYV7ASUROblDs@jE!-PXrN>tu^_nwQ$#B|>sl2s8m+G35MPH$&f%mBc!V20@4i>kP$n+YHD8;yhz&L&HIXy9NQ^=mp40HCem`ni0BY(~W=~5U{u`I;;<e5I`?rI9iM8!;G#j$p^IU2TXcj1r8k%ytK&_6a@+g-Wp6Dk$Hy=9MRPXQaQHFp?y$T_H{SwY+&!N)rY0bjkE5yM>cf+uz;yIUJ^l~7>Ym;wS@vVD|J09Q^gSQ46dOd<~!<41=qmMolB<^SnHr~6ji9}`fcs}F?7!B36N9~3d7+iXvLHc^e92b;rli;LCGQ8Mge0m>2TfceMS)L8j2%y4mAfPKtp%iZHON01PKB;I2y5xfOL<K;X=bFyo(>X5QfBQ!x%PB7YX`?DCb8DW;@gn>G1~qhY=lHXzq0gK9kO25hG$N&_6a39dK2<m}v7x_8Wc22dxf^ZcvHx_QeEr9S2z0KK_Hr2#HHje#$`lF$%$K%>}s_p92~Ml%ZvccZ4KANkV@&x`9?h5{*zWAy+)5_6}|=w!+=k4?@uCX+<I2Lj1r3J-h%nXws;4)DjFNzoy;oS4Jt%hW~*Hb1lXpL!{dKyI_pXxviUP4>o*xS$2tQEN2(aQoEQZzJMJ&9C%BLEI-nFI9L^24Gy3dlx}PsB!CvKa(1+Z_Af4&#tfl!I+keQnP@~;*ypr{?Ot-#QDHPa0k{KTbWyLiw*w<e_H;)HRDFq9YrE$nzMKreAz*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