Problem:
Score : 600 points

Problem Statement

Find the number of sequences of length K consisting of positive integers such that the product of any two adjacent elements is at most N, modulo 10^9+7.

Constraints

1\leq N\leq 10^9

1 2\leq K\leq 100 (fixed at 21:33 JST)

N and K are integers.

Input

Input is given from Standard Input in the following format:

N K

Output

Print the number of sequences, modulo 10^9+7.

Sample Input 1

3 2

Sample Output 1

5

(1,1), (1,2), (1,3), (2,1), and (3,1) satisfy the condition.

Sample Input 2

10 3

Sample Output 2

147

Sample Input 3

314159265 35

Sample Output 3

457397712

Solution in Rust (1.15.1) (judge verdict: Accepted)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use contest::scanner::Scanner;
use contest::vecs;
use contest::modulo::*;
use contest::modint;
use contest::misc::CONST_1E9_7;
use contest::query_problems::Cum;
use contest::extra::VecExtra;

modint!(CONST_1E9_7);

fn main() {
    let mut scan = Scanner::new();
    let n = scan.read::<i64>();
    let k = scan.read::<usize>();
    let mut layers = vec![];
    let mut i = 1;
    while i <= n / i {
        layers.push(1);
        i += 1;
    }
    while i <= n {
        layers.push(n / (n / i) - i + 1);
        i = n / (n / i) + 1;
    }
    let m = layers.len();
    let mut dp = vec![Z::new(0);m];
    dp[0] = Z::new(1);
    for i in 0..k {
        let cdp = Cum::new(&dp);
        for j in 0..m {
            dp[j] = cdp.sum(0..m-j) * Z::new(layers[j]);
        }
    }
    println!("{}", dp.into_iter().fold(Z::new(0), |acc,x| acc + x));
}
*/

fn main() {
    let exe = "/tmp/binE68745D5";
    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$0RR91Sgk<-00000KmY&$00000000000000000000Kma%Z0{}n(000000RR911poj50000000000002M$00000002M$00000pSA%200000pSA%200000001BW000000RR911^@s600000000000Kh>2000000Kh>2000000000000000sN5j{0000001yBG00000QRQ@G1^@s6000000000000000000000000000000000000000000000000005C8xG00000+&hJ7RZv(VR0$0h00000poIefpoIefkO2SymjD0&0ssI2`}-mPe??420s#R40suY$4G;rB4;%7r76ky{fdc>&fgQVhH~<C(4*(7;1pojoAy3#q2XJ5m0Nd>Q&L99c1|@432V=rMJ0TbrEod<SH^Bz7ZU+MdH!v;o`<AfCH2_fMbYwTo7ebzpZ3jcN2>=DQ8EgbMQ3e12gatc!5CBqdr!a(seZUj|2Y~<p00000NC5xfUIPGRr2zl}Neux1{|E9=Si=B8S3y=Wz(G|(R7r!(|5Z~-x3~ZQiT+H9&rXdj0!V}GNJxn^Bm+z&2ovE<oBMBf2PpEc4pbx<NQ;ytfISoU{*SzE56BISB#1;LAV~MnN{t*K|J&Q&K^!Yhje7wTTqF<#{^$(>l^jTgz*_q?_jG<ti$DY_iN`u%@40r@3s^}3#Rn=`OWL-5Ya0)V(etDP!4h<UwzX~h3C;rV7ugCCw0^exZaYYgIXp!|#snAuVPsrGZX4{`gg%Rmp!y%~rf>hZ??H*gf?U<aNJNR?TU|k1K?7bvUz>k-|HD;GjSV*L0!$76?FJPf2?I5PZw<e94MDhY0gUBS4hR$lglYD+6}lr_7%~&zPy%nU2itwOdv1ILQ=TLkiF_ms3{+(V_GfqPW+(=<h>H}a<w!B@G1=Sg-RE87{J;M$<nR>$0g_zXySLj{1B*9}1zxj;iw)6xYDGBw?%OfR7d;0M0Nw&p@@9}#uyg;~cCL_tYnzQ7@P3nqt-<|${}n%coCOGf25KEvS+?%>_yG@uU=ZoD@C^fxb~Ai?19#~J5hA|`A2U09EckZYFD4NtMHre0cu&VmzAtPqI*d2QzW^X864`d|#t_&h$GR3KG4>mVIrhS`4_7JGP`@Zw<9e<A87?=?9uYtg0~HI+-Q34OIRFnREi$mcuHj&C47abgg9dwS9UVwOZbOV*CfY~rYp+y&2y8J535VNeTiy$076@c+Q^sz(j!Ppw2n)YRiCMy1M?lfTcLfHrVf@Yazln)x5XL|lI0y@gLm7!n9A@pkZ7q9q$3rOJE1qR(zTYfEFvdebDL_L(4hSdwL`8)5bSYPkQs{YZ!F@=H1$BKA$VLVr2f=M0c#u@Rd2eg6Ehn682Xx2>+u<FS$IvN=J`UIzv4>z5D*>19J3dT0jhqo8G162OjB40o8%eBA&um1EYr3snL@36+)l3O6Ff_K^6`mMLEgWn~kv>zubbDhoAP<KU1`>Kn52McydbaVsg9|VLMZ9H;tpESNNo9}+g~@a-iU+d+vH?6RbP7Bz4~2ezp>;EqhZ^|-bQXlt-v;fi?YKGNLIL@G2AV50u-|6k?Q{kK!-U%~5Wd+hERmg8z}(aZ<gk^`#Zyy`T~<OXw8cTT?zg|-lh9d!KPz<%xyJu=PE4^S_tM7e1MK>SLAeSez1wXO_+~B-AA~vwL_9gp-1yu7AKXC?wj2tB!_b5K33nER=t=kCa1OrTUFi3T)`P+J#dFk6g~0LA76x;eUODoKN~i)q91+xmK1sfrf8QbufB_W{O*!;p2qV33a(xdMz9dCO8VKteO2**=@5co07QMv*6KocE8{_}QO>hn1NSTfOSZ{yYp~dwGFiblh5OvP5-4!D602Yi^12XHnJ?+C^sXz@j1UWq#4}uD|{r18KggL?K1}@4-!RiDdBo=#re-Asp0<VMm3@`^!=_)`jkV`KA_^)k_=R(Bz7byC$@RYFE<X_QrdRj93KfJMy&@zMm3DX3IO>5)|4}b}K-{9Lu!U2i!J;ZU<=?_8S?t@|WW?Kb)5Cwy}9hb4!+*eJPPbxGQ{aOHXP)<rvNh$B=II>RGG25n11d9*1&9#A%9XH84Kr$%)1RdONd_ECs;Sb^F1UV!>nr?F&$?_f%26PcwVdGy1SY8*44Dm>b!2{b+!0-e#g;|Fk><JVW+CqX*1kG5nzGr+akzmtM#2Q?4IRbfwY{ST~$X6gk^6JR?|NQte9AIrsIpskKHg3b$VTr~=2pM%YElb8<!VsjhkV=Uh?u!UG%(iC7{Wj-6OWR;2`J1HrihRLtz`<Y>`C6n%DeDXqXWY%h0kf*Wv-Akuj+P$%|6+egxH~J&hB8$87@1YbCTy8uB>7@2WNqOT1AJO!%oS^^B{3%Ojn>`Pm_BG0>M$3~Oh9ZK+X#5}cMuSyBJF=<X-S+UzvYjj5;0$JiEx2GQlz}@D+|;~jYa|OwpQZr=ug1w7~gyi_{Fwl|7AObB&a7gz$d*!t&16`P<$vhyN6thfeaH<V3muUJN8Ipr)ED%Iq?5CNNW1;7MctUh73qai!Ag=11$G9woAmPNdf8z&`#(-w(#F>1Nt2e!boYt2g;f|AjLJ=f34V^3B@Ok1S&`c52fi!g;?4y_{cRj3X{N6Quh}LAG#}AY4&x5*jP>ToNr^{3&1VzRnm`!?6!?<6xNtryBvorA7WN$fgJ(biuPU;c5AnD_t+9-fy0vuwDesd=oCu;(;;lbbD=2h0m@w2+48;3>RiFW63FmuuvQB!#9Ywu0t@z*E)TEED_rTpj;~9J3?V`Rixsf&Yhl7V#fb`hQpw;gH~2aUoJ)mr=?bbfw!_RyRrUS=UaHi7Tfy%GI)QwH<^hG)c8~`R{8#tXi=l)Mf#nYaT>yGYn6M4jjf=M$6k!)i9s^AXB#oKHRtQT0WDv=T4_h)_%>Drk45v?=AnaGViOZ!4(xVFtAm>~taa>I;XWNU9I)n#_u=2^-BZUP)5DvKF&H}owi#G@*$Pfnx8f0xG8s4@%CBTva@gWcDA0FY01SNWnn8>MvI{<Wh+dX=1Y(I>Y`b}(IdszI!)F2pG0wG@)Y&Kvwf*x=cc<Uk*tN|7fJybULy@Op(O$^K{0d;&DKoCYSM0i2$>u~!%N5}O3ZaX>+9zp~Ehl_Iv7|3_S_LLP2Ly!&TT!l<q$siYuOn~mBp1S`~I2ekPAtk~4)KfSl)jR}!g=`M2sPiCrT(ZX&NKKdrbR;15Y%DewVy%z*fGQ#!`|kta54#T#gboiWZaF(x5VeOm;|nMox$9mX2{08x5dk<0_JBaP{%fh(rr<3R8ympwFad=(aJa7ByblXsX2xo^^N52}R1OeZ;MJM?*PQ9;4STR(psu&i&v4*2nnQMUKdokEfCYDM@S?kSSm^aA><tqRXc%nOqu&Q^(3Nx!_0R#I?Nl^Tfy6vpUZXHb1zm&%D1;6hJ`t2KQe2oxqwQ+<4UQEKh`)AQIzOA)+-|~KKP<!$eJIA+Ha1}sX(ZMH@)NV$CwTR(Sx#CSz8Rfd$;sG0+!@<s!Dr-^oHAL$XwE*sk}Ffb0T3Vu*Z|LX)NgSHZGN70rPy}LH|{qhCR+TxVC6=&N?Wlz*s%BkzX<<LzbFu87m_1LNL*bZ&&k=k1`<Cp1t+X~HU`>PS%@Fn?5rU)Bx4y>W?(E%aDx8)3mkJC_yz0l?4tO;4IG3XBjUbp1{BHI8E^thz%Q@|B7+PvppbyG&+|FB1Yl4=$2y}R?Y0C02ygpK1_M{EM0+&>TddQ5ir6oVaX7yVwBAEO|JJ_;48iFv2pA9#pwT`$_&pFdAP>K7m(0v+srDBb0(4crzQ6JMetaOhin${0xSD&I*$M?IveOk>f)@<Z?hsHI0DK^hrmkzIVp&#oEKDOK>}a$QWRLH^1Q$-M{X>FkZWQCk0BvC#%Zp`hK@tO^4L135v|%`Q)9i^S=o^7Z5Q@wwl5jv^tOG+^%zz+k;s7H=2=1YdAHnzOt@I3d2m(VD8l*T^i_K#9OKqPNHZT}6Rcj(u@LH^GDM+1<tq6=ch)p(FG`|D4ZXs1;dwXtl6usZ>c2*z`2|;@x%-D=WAW_>8he<Ve5J7z-47{M5>7+v$><Mv%Y)JcQ2-593>%!w3SGh10U|bD&gm)8*1rTkC19fTK&J>edNcaFuYFV=n*3t|%6I<&d4@n4YOFa{@@J}z63JdT^8*Z2L7tRgoVR(Ue!?R!lVsH-#zD9i2Ezkd3Y{s$yt2js6{UDwJQ%viDJB-LLZD&@5pEXA>+k6iT?+WC|u|o^KW?EcxTpZgiIT$7L$57;EGPYaNCK(~2KT_F*Omb@wLXbD4CExTvC%^Q(K}h-_JP!-cNQ*}Z4bXsJ_bKtA!xn9TEw)<@^PAJU7IstvwgQ$^487joMY{$MM+2fEO^ZGU+jKF8r7#s0{|e#)zV2IWCd9tvb#m!5XB|V(__7hoR~lFAXfMTT5u^EB<Gf0@ax0`EEofAAOf%VBb0wlCH&qoUWaI(1>m@J!XB;qgY(EoCi6&uQfW!z34zVD@er<t@g#^L)-@Gl*$<Bl9{7(ZpPY4H3-+n3=dQZ+t|Hcs)dvM#TPy~}YO#JY=j(rIplBoCM4}cqq`?hU_12cmmjw6k34KnoqbTqzmrp{)!3%dIF#e;PX7nU6&a@p8Q+d~>+WF{sZfplBx$aTQU6JZbtEy8wV)OQ;U7V9Z9Et8BK-)1c%E6^nIumW=)5Oc%M2BB+2B^DUI*Z=5v<T9{v6}etYD2#v*FbhFHh*R&D%GbF-2ZzDo*m-h1GxRH^@9EePvQcH(!4O)7tb=a#{{nI)TzCJ;%2ET|t+ouPgTknA#U5gRImUJH>k1$@2OEUjg{>D<4()yj21XF>GFej$mVCzNZZ}>FotwOi9|C(2wa(btgp>)&udbV=yV!IJ5Foipiw3y+*><65jdc(TK3-n`C7vtB2R0TA!~Q@3!%q^ojY4-9uvx<|7#Jf<4{x?h6B-WJC(mveghsc}z3l^jAolom2bd5bK??}C+b4e+>KIc914|I+{DEDjZh$>3QV8=8Z*YOz2#x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