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 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/bin8D0ACDA1";
    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$0RR91D6ByM00000KmY&$00000000000000000000Kma%Z0{}n(000000RR911poj50000000000002M$00000002M$00000Z?ypc00000Z?ypc00000001BW000000RR911^@s600000000000Kh>2000000Kh>2000000000000000sN5j{0000001yBG00000QRQ@G1^@s6000000000000000000000000000000000000000000000000005C8xG00000-8=JdRZv(VPzend00000poIefpoIefkO2SymjD0&0ssI2`}-mPe??420s#R40suY$4G;rB4;%7r76ky{fdc>&fgQVhH~<C(4*(7;1pojoAy3#q2asO_0Nd>Q&L99c1`THy2V=rMJ0Un4Er>M$H^Bz7ZU+MdH!v;o`<AfCH2_fMbYwRy7ebzpZ3jcl2>=DQ8EgbMQ3e12gatc!5CBqdr!a(sec%`X2Y~<p00000NC5u;UIPHzqX7T{Ne%%2{|E9=Si=B8S3y=Wz(G|(R7r!(|5Z~-x3~ZQiT+H9&rXdj0!V}GNJxn^Bm+z&2ovE<oBMBf2PpEc4pbx<NQ;ytfISoU{*SzE56BISB#1;LAV~MnN{t*K_S@UvK^!Yhje7wTTqF<#{^$+?lTT~E=Kh7ibbd^WKm;m@$2wp=*X~*iSV;lJ2P#?Hwr}lA8xM)m^P~j95_EvJwryVt&I0cj*$NS~cHeEsen^cuJVipr1Q-BeV=QfhJ=;TsK8uW?`XBE0f7{)rL5aj5lq}W6NJNR?TU|k1K?8hj_y1l&U&B>QjSZIV0!$5G1{Ht^12z1<-8JIu4MDhY0gUBS4hY*;=)M#MWMv~<7%~&zPy+Ye?%8gE2W?CQQf?#|iF_ms44>V#Z&Nh{HYf(OSc?>;wMcKbciS=TG3Q<5{J;M$<nR>$0g~_DZf9Iq1B*9}1un9Niw)s>c;{|!YDF>07d?l`JyF7DkZs%UU#(M6fIk9r2*?Oqz{5@ZzrAn2^mhnJi#`HI2>%cT8+Zr+bP4XmzIPM<6?1&BdoTYbVi4IIM)+nf4<Cg8P!(MK4+{@=JHjq*7`z6dWGKE7deE5hJpeRpB1A7Mg~KDf4T0?VfCZZaAI&#6cf&BgC;-0=1awY&gZTf?E&SULggOO64_Cks5tqOk2L>5rkg%YTfIiQ+MM-c3U{FBEjQ!BgIs^iMTUr5cII&P@FDNxpX{aGajllk6yf`?&3pL&`(n0^$zXuHG*l1sVDKJ{cbK`BJZL~R15H=O|slM)S%UpW)7Z?I`RlWcnzaYA1aG&ne0J$O_xc>l!DeJz;%tF(}f)G#`FFLom*;ze_d|6fnxZPpsEKKzJJ?VW5zXU&4az_{5c|!z3T*m-yVPCBL*lBLd4=4pwu<k=RhwY^ea?kvW#}5$v=ohbhYqlu|&}4x;B`A^uLp1l;+XUMWiv%TtjesB)4*qD~Ht4|tW62MWZ3zMog*I#N>k5pdI4W#QZOD*qEuU>rRqM5Hn+%vKNT?u>SjHaVtxbbF09d923k|n$BvoU3Xh{@yw{LGRLm==AC;@c|L3<#~)QoLiJN!c+Ni}~2L45>|x2-Mti5w;au8kc8rp|X3N=hP&2x7Qndl%z_Vg{rzs9!9J8^7@0?~4VHD~SVjVu{#@#9?<bJzLJqYR)WS5BBWcnFHJFA`gkf5(F{uWA<%Z<}a2CQBarfy!DQB2hsh3a%r3hzDC34mS^-+?8d9aFw*V^VK|ooQjF_}G-lT%gz~I81b0U-*No_~U3qrC0T2QVDj&^Xwp((@acvkLu+~Xzx1>3Ob|x9GuQ;;_nPgZHDuQiEOTL*nC)@`i0;kgeRj{rVXWp-aaKw6EBX}1D+z;D_h6a`%Pyzi5)fFi2UbYRqMF0+u2b<{=^}h&VJIOJ>9(N1*Mi`%6V8ge2bWq0_H+*Eqzja)4I|eBAcErcJB=^)J9S0j}M3ckI#vU-gC|AZV3<|EXX=5xgKq(PgKp+PlpPRHTGGIptF^;W+M+=UUBZF*>zV@~T8AU*y2xA?aZ3e~)-}?(u76?t#bZ$^(JrENpD;x~S*uO}CMH_qhzB`+c;;cDX5XL|lI4JLpjlV02MHz`r91(rF$3-aCG~eI8W}9FI5k)Y@ML;MZBViE!vOz>eg!XhQPL4^qO~?V%btnP_Q3!5x$M8KO1|MXQOKEEXIjMCg?O=+z!tCj2&v1V&eaDXOunl+$9PbDXob?9&La+*e+es<IeJ4I`<nG;kaWF^^ZomszwgSjKZEx7RYy*F^5bOy-bq=q?c>9_tl(`5GD}37zi2W01Zx}{NxBvhUmV^5Q4}!aI-_{=(UcpAgLShBHt5XkLoBQ3^1;hs^Ru#zd4_L^f22tDF*tfw05Dh7<8qf<|(egJewtXM$!b!STfJ`ya5$GN+Ujp0M_76kodF}S9jM&Sz_+pD%^)dkj(YC=H-vT-Bb{^jt_Z9ftyX{sliTxPIBy#8L9|riHtQ*4X8aP44L;>i#1;+j>ImLJ3$NeFV$Fod0++Mdi49CFBdqu%yV8iP<a0In4P;4-Rcg*Vc1)N<Y_6ZCIBUS<gKr~k5*S#(qP!d=Hz}5sFcu+hBU>k%MTH7#SpcH%$3Cna&3mufyGHCI?Q+IVmw%CZ)UBBCYRAFKuy}4%Hk40$vt?b9?Ko6Y8)Xu56(O&lC|0GD6@LvJfn&Gf*2Y>V6&kWHsk6qZ`C-Hp3>oK@fko8T4$rsu#W+#0)=v)f{!Egv0atP{t-!Y80!2A9AO*zvj3hJMMy6fJyfVm(~4cLN7_xiiQNFTWW$6qXh!U3jW7u@0Yzn^Xa)}Mdd7P`a8d_*fbv=2|nNjd6b?(D~Py@MFOTE|^dbnb22HU5UiMuWfstun}qeQQ7X4^GcO0y*_{+BKHe0>=AmLAyI-LV>oiZS4F1i(ow42znLJWs?i}sQbgE*a%}E>vgSfzwEwgvleU%p#Nz*2<~Lhwt779PlLz5iONqk`(~EV!3sJ3b;rL#%@Mc`E5+o@W*LkO8N^x}XXx!Q*l;#HD#kt1&Np(0g2BEcFTDYd>}AJ$z6dnGC=f`^v0X?>xw3)ES~)aNx+NKNFl#Dd-^qmKt}`DQ5wLSItCY{U6pV&2Upk9Nx?Z^8$_^><4bcyS#cN#sTG$Trg41#hhNgqIaN9%-NIBUsM+3kpY-qG0P3`V<F?6k6C{$Vb2jXyHCc(Gig~VOtb#hD%cO658ftQW@R~lFANEIs;sfj9=`3v33ts@~Vaa46o!z9~muDK*8H&qoU>m@HAGV%cZa2yj&iDnU`wkBa-b(<F<RuQc(Sq4nvg~S}KL;$a<z$*ieaL^Tr_f_0O2ssn%TBD7Kd=Qd#Kn$E?b*~SlIL3JdNN6B-@EC0bbU_nLii<n~d-Os-b`G1LWF#W`AG{UboHGe6d%=nZJvqWQ2ynaW8-0KP(cV1VpdC98wmo!f2v#9U!a`pi(+**7x)1>W{~d{nJONq}T8&NjfcXV-!$5%j{sR2=AauPzFU3HF?RnqANWtm`LbiRl-48S>&He_)5sgR`VthaM{STwUa+J0KI2R9dzX8^O0}lWQBM55SxBsTU$#f=)A3(JMvMBp2bO!`2!KL27bw0#{`2lnq(sbd&eY<y!S2O|n>n|e)28*T-xpIMTfA0~XzAXqm4TE@HN-b?igl`o3G23QuU35~Q_P@EUGE2}wqzQMqNNd{)aI-b*w^psBAT0B7-0P;;xo+$hG7ldwBG4Bwwl6pGEsKRI)G00A9gMa*YYsB)aSq+Y8{zN|;~9pQnO$uT*h~=R*5Eseb=ZVhgcQ?c)EanW{fp>8h%7MYi4m9XutMC@8f@z-5emp-I7Emv31K@M2-G!14RqP|_S+&6w#Galcc8fdKAg1ELX5z=!Gp;d9I##5cqPS$y6Q`=TXqP={SSP|!FCR0jOhp|3{C9+OAimX=rG=i>%r>=gXKTL<p@3)Cqj0*0#c3{xc6W1jZp%Mjg%e0fFt`DA>VJj^Ja+@2y^it44BP)a}a>Zz=(xgD{NCBq<90(fOI7z%pC97mjc7Kma=}f1R!)h-6X!aAZGdrZdiPBq;~Um#>X&KP`)dJ!0m)sU>CXu3%t@CfnyQ`!6klSEBFstUuKZQFHrv%F~C{FX0SpwB)<<%2m=c+e%D04(RFO%jc#8?1Aa9*_;m;N!F>U^5CU>R3mFpH7<;T)-BajGY!CrD9R9r30Uq-YZ~ZNGI`eD8;cp&)MhHpA2KWFIDx_IADuCJSxdBU)EEyt#fgtHmZ##NQFMh|Q)<Yn)K5V~j3w8f}I1g~ZPG(6N#1_PUFQz;sNp1fS2GE;>r8f!|-=S_)=exDQYzUaz*2hKb+_wu6l#6qkIsS502sam(+B5-<G2|AJmBiZ&{98JT20@4i>kP;O;yi@G{c|&FLl{f};OGUnKr__QNAwZ8X43-(7J=fpTo3{XusYmdV3^VM;W%20F3AV9z@a03?FUSH5$xpQ!27Go6ckEK9g%q>y1GDz2vTXb{0hsyfuVIb>ug}}l)14Fuhp~ewnr8)^{_T{H;xiP77F|yq8N%m5IhfcJu6eiGq{G<5Fq9|>P!U#H+RBIrxRG~pl`10w_Oxf?kq8M&g%(~R1pflpcSLT#114VLEF#-g~s9eA=^d)V|BOp?J(&^5bGL>BXkZm2MyhA!z68p9_s`N0y#LuG6Dj0j|&Z-XurIRAGr{Ql-M|3glWSG%7!Q{nC)Qa)DXGx21ayjO)O~cbqGGgLZpZto+|*3=zt{#1y$>q>N~cPX!Aw~tqzNBP>J^Ow_hUm#RPO62ZPB7iAzv^%0O!_z{2`53h5}H0~%Aj3uXkAgd{(C4YUd^LVrUNjoLf7{ZKHCa92Dmw!+=k4?@uCg>V~{X&%4>Z3}P%M-8ZT)Ito}-G0R+zji6lhW~*Hb1gDNs%^##ykNY|y1Dicvo@@GS$2tQcHu15EbEvjzJMKpx1@MGTyN5QgH^%B4Gz#2#-%}m#IP1&i*~f)f@$o9_6*T<I%a615ex9(2<PN`$yH~DQDI~~0k{KT+TISdbWu}E_H;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