Problem:
Score: 300 points

Problem Statement

Takahashi has decided to hold fastest-finger-fast quiz games. Kizahashi, who is in charge of making the scoreboard, is struggling to write the program that manages the players' scores in a game, which proceeds as follows.

A game is played by N players, numbered 1 to N. At the beginning of a game, each player has K points.

When a player correctly answers a question, each of the other N-1 players receives minus one (-1) point. There is no other factor that affects the players' scores.

At the end of a game, the players with 0 points or lower are eliminated, and the remaining players survive.

In the last game, the players gave a total of Q correct answers, the i-th of which was given by Player A_i.
For Kizahashi, write a program that determines whether each of the N players survived this game.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq K \leq 10^9

1 \leq Q \leq 10^5

1 \leq A_i \leq N\ (1 \leq i \leq Q)

Input

Input is given from Standard Input in the following format:

N K Q
A_1
A_2
.
.
.
A_Q

Output

Print N lines. The i-th line should contain Yes if Player i survived the game, and No otherwise.

Sample Input 1

6 3 4
3
1
3
2

Sample Output 1

No
No
Yes
No
No
No

In the beginning, the players' scores are (3, 3, 3, 3, 3, 3).

Player 3 correctly answers a question. The players' scores are now (2, 2, 3, 2, 2, 2).

Player 1 correctly answers a question. The players' scores are now (2, 1, 2, 1, 1, 1).

Player 3 correctly answers a question. The players' scores are now (1, 0, 2, 0, 0, 0).

Player 2 correctly answers a question. The players' scores are now (0, 0, 1, -1, -1, -1).

Players 1, 2, 4, 5 and 6, who have 0 points or lower, are eliminated, and Player 3 survives this game.

Sample Input 2

6 5 4
3
1
3
2

Sample Output 2

Yes
Yes
Yes
Yes
Yes
Yes

Sample Input 3

10 13 15
3
1
4
1
5
9
2
6
5
3
5
8
9
7
9

Sample Output 3

No
No
No
No
Yes
No
No
No
Yes
No

Solution in JavaScript (node.js v5.12) (judge verdict: Time Limit Exceeded)

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function an(a,b){var c=b.fe,d=bo(a)-c|0;if(!(Tn(a)<c||0===c||0>=d))if(64>a.Va){c=X().Hf.c[d];var f=c.g,g=c.h,h=a.x,k=h>>31,m=d>>31;c=h-d|0;h=(-2147483648^c)>(-2147483648^h)?-1+(k-m|0)|0:k-m|0;d=a.Pa;m=d.g;var n=d.h;k=x();d=We(k,m,n,f,g);k=k.v;var q=x();m=Gf(q,m,n,f,g);n=q.v;if(0!==m||0!==n){X();if(0>n){q=-m|0;var r=0!==m?~n:-n|0}else q=m,r=n;q=(new v).f(q<<1,q>>>31|0|r<<1);f=(new v).f(f,g);g=q.h;r=f.h;(g===r?(-2147483648^q.g)>(-2147483648^f.g):g>r)?f=1:(g=q.h,r=f.h,f=(g===r?(-2147483648^q.g)<(-2147483648^
f.g):g<r)?-1:0);f=p(0>n?-1:0===n&&0===m?0:1,5+f|0);f=vl(X(),1&d,f,b.Me);g=f>>31;f=d+f|0;d=(-2147483648^f)<(-2147483648^d)?1+(k+g|0)|0:k+g|0;0>d?(k=-f|0,g=0!==f?~d:-d|0):(k=f,g=d);k=Yi(x(),k,g);(void 0!==l.Math.log10?+l.Math.log10(k):+l.Math.log(k)/2.302585092994046)>=b.fe?(c=-1+c|0,h=-1!==c?h:-1+h|0,k=x(),d=We(k,f,d,10,0),k=k.v,c=(new v).f(c,h),d=(new v).f(d,k)):(c=(new v).f(c,h),d=(new v).f(f,d))}else c=(new v).f(c,h),d=(new v).f(d,k);h=c;c=h.g;h=h.h;k=d;d=k.g;k=k.h;a.x=xl(X(),(new v).f(c,h));a.Kd=
b.fe;a.Pa=(new v).f(d,k);a.Va=tl(X(),(new v).f(d,k));a.Jd=null}else f=Ef(cf(),(new v).f(d,d>>31)),h=Zn(a),h=Ee(ao(h,f)),k=a.x,g=k>>31,m=d>>31,d=k-d|0,k=(-2147483648^d)>(-2147483648^k)?-1+(g-m|0)|0:g-m|0,0!==h.c[1].u?(g=co(eo(fo(h.c[1])),f),f=$n(h.c[0],0)?1:0,g=p(h.c[1].u,5+g|0),b=vl(X(),f,g,b.Me),0!==b&&(b=lf(R(),(new v).f(b,b>>31)),f=h.c[0],h.c[0]=kf(of(),f,b)),bo((new ql).Fe(h.c[0]))>c?(h.c[0]=go(h.c[0],R().ue),b=d=-1+d|0,d=-1!==d?k:-1+k|0):(b=d,d=k)):(b=d,d=k),a.x=xl(X(),(new v).f(b,d)),a.Kd=c,
ho(a,h.c[0])}e.li=function(a,b){ql.prototype.a.call(this);if(null===a)throw(new si).k("unscaledVal \x3d\x3d null");this.x=b;ho(this,a);return this};
e.r=function(){if(null!==this.ne)return this.ne;if(32>this.Va)return this.ne=Ve(Ze(),this.Pa,this.x);var a=Zn(this);a=Xe(Ze(),a);if(0===this.x)return a;var b=0>Zn(this).u?2:1,c=a.length|0,d=this.x,f=d>>31,g=-d|0;f=0!==d?~f:-f|0;var h=c>>31;d=g+c|0;f=(-2147483648^d)<(-2147483648^g)?1+(f+h|0)|0:f+h|0;h=b>>31;g=d-b|0;d=(-2147483648^g)>(-2147483648^d)?-1+(f-h|0)|0:f-h|0;0<this.x&&(-1===d?2147483642<=(-2147483648^g):-1<d)?0<=d?(X(),b=c-this.x|0,X(),a=a.substring(0,b)+"."+a.substring(b)):(X(),X(),c=-1+
b|0,X(),a=a.substring(0,c)+"0."+a.substring(c),b=1+b|0,c=X().gk,g=-1-g|0,X(),c=c.substring(0,g),a=""+a.substring(0,b)+c+a.substring(b)):(a=(1<=(c-b|0)?(X(),X(),a.substring(0,b)+"."+a.substring(b)):a)+"E",a=((0===d?0!==g:0<d)?a+"+":a)+Cn(x(),g,d));return this.ne=a};function io(a){if(64>a.Va){if(0>a.Pa.h)return-1;var b=a.Pa;a=b.g;b=b.h;return(0===b?0!==a:0<b)?1:0}return Zn(a).u}e.f=function(a,b){ql.prototype.a.call(this);this.Pa=(new v).f(a,a>>31);this.x=b;X();this.Va=32-ea(0>a?~a:a)|0;return this};
function Un(a){if(0===a.x||Xn(a))return Zn(a);if(0>a.x){var b=Zn(a),c=cf();a=a.x;var d=a>>31;return yf(b,Ef(c,(new v).f(-a|0,0!==a?~d:-d|0)))}b=Zn(a);c=cf();a=a.x;return go(b,Ef(c,(new v).f(a,a>>31)))}
function jo(a,b){var c=a.x,d=c>>31,f=b>>31;b=c-b|0;c=(-2147483648^b)>(-2147483648^c)?-1+(d-f|0)|0:d-f|0;return 64>a.Va?(d=a.Pa,f=d.h,0===d.g&&0===f?(a=X(),b=(new v).f(b,c),c=b.g,a=b.g===c&&b.h===c>>31?ol(a,x().Fb,b.g):0<=b.h?(new ql).f(0,2147483647):(new ql).f(0,-2147483648)):a=ol(X(),a.Pa,xl(X(),(new v).f(b,c))),a):(new ql).li(Zn(a),xl(X(),(new v).f(b,c)))}
function bo(a){if(0===a.Kd){if(0===a.Va)var b=1;else if(64>a.Va){var c=a.Pa;if(0===c.g&&-2147483648===c.h)b=19;else{Of();b=X().Hf;if(0>c.h){var d=c.g;c=c.h;d=(new v).f(-d|0,0!==d?~c:-c|0)}else d=c;b:{c=0;var f=b.c.length;for(;;){if(c===f){b=-1-c|0;break b}var g=(c+f|0)>>>1|0,h=b.c[g],k=Na(h),m=k.g;k=k.h;var n=d.h;if(n===k?(-2147483648^d.g)<(-2147483648^m):n<k)f=g;else{if(T(U(),d,h)){b=g;break b}c=1+g|0}}}b=0>b?-1-b|0:1+b|0}}else b=1+Ka(.3010299956639812*(-1+a.Va|0))|0,d=Zn(a),c=cf(),b=0!==go(d,Ef(c,
(new v).f(b,b>>31))).u?1+b|0:b;a.Kd=b}return a.Kd}function Wn(a){if(0===a.x||Xn(a))return Zn(a);if(0>a.x){var b=Zn(a),c=cf();a=a.x;var d=a>>31;return yf(b,Ef(c,(new v).f(-a|0,0!==a?~d:-d|0)))}if(a.x>Tn(a)||a.x>ko(Zn(a)))throw(new wl).k("Rounding necessary");b=Zn(a);c=cf();a=a.x;a=Ef(c,(new v).f(a,a>>31));a=Ee(ao(b,a));if(0!==a.c[1].u)throw(new wl).k("Rounding necessary");return a.c[0]}function ho(a,b){a.Jd=b;a.Va=Pe(Se(),b);64>a.Va&&(a.Pa=b.Sb())}
function Tn(a){return 0<a.Kd?a.Kd:1+Ka(.3010299956639812*(-1+a.Va|0))|0}
e.gd=function(){var a=io(this),b=this.Va,c=b>>31,d=x(),f=tj(d,this.x/.3010299956639812);d=d.v;f=b-f|0;b=(-2147483648^f)>(-2147483648^b)?-1+(c-d|0)|0:c-d|0;if((-1===b?2147482574>(-2147483648^f):-1>b)||0===a)return 0*a;if(0===b?-2147482623<(-2147483648^f):0<b)return Infinity*a;c=fo(Zn(this));b=1076;if(0>=this.x)f=cf(),d=-this.x|0,d=yf(c,Ef(f,(new v).f(d,d>>31)));else{d=cf();var g=this.x;d=Ef(d,(new v).f(g,g>>31));f=100-f|0;0<f?(b=b-f|0,f=Df(c,f)):f=c;f=ao(f,d);c=co(eo(f.fh),d);b=-2+b|0;f=Df(f.eh,2);
d=R();c=1+(p(c,3+c|0)/2|0)|0;c=lf(d,(new v).f(c,c>>31));d=kf(of(),f,c)}f=ko(d);c=-54+Pe(Se(),d)|0;if(0<c){d=Cf(d,c).Sb();g=d.h;d=d.g;var h=g;g=d;var k=h;if(1===(1&d)&&f<c||3===(3&d)){var m=2+d|0;d=m;h=-2147483646>(-2147483648^m)?1+h|0:h}}else d=d.Sb(),g=d.g,k=d.h,h=-c|0,d=0===(32&h)?g<<h:0,h=0===(32&h)?(g>>>1|0)>>>(31-h|0)|0|k<<h:g<<h,g=d,k=h,3===(3&d)&&(d=m=2+d|0,h=-2147483646>(-2147483648^m)?1+h|0:h);0===(4194304&h)?(d=d>>>1|0|h<<31,h>>=1,b=b+c|0):(d=d>>>2|0|h<<30,h>>=2,b=b+(1+c|0)|0);if(2046<b)return Infinity*
a;if(-53>b)return 0*a;if(0>=b){d=g>>>1|0|k<<31;h=k>>1;k=63+b|0;g=d&(0===(32&k)?-1>>>k|0|-2<<(31-k|0):-1>>>k|0);k=h&(0===(32&k)?-1>>>k|0:0);b=-b|0;d=0===(32&b)?d>>>b|0|h<<1<<(31-b|0):h>>b;h=0===(32&b)?h>>b:h>>31;if(3===(3&d)||(1!==(1&d)||0===g&&0===k?0:f<c))b=h,d=f=1+d|0,h=0===f?1+b|0:b;b=0;f=h;d=d>>>1|0|f<<31;h=f>>1}f=d;b=-2147483648&a>>31|b<<20|1048575&h;a=Ia();b=(new v).f(f,b);a.ie?(a.sf[a.gi]=b.h,a.sf[a.si]=b.g,a=+a.ai[0]):a=a.Nq(b);return a};
e.ji=function(a,b){ql.prototype.a.call(this);this.Pa=a;this.x=b;this.Va=tl(X(),a);return this};e.z=function(){if(0===this.tb)if(64>this.Va){this.tb=this.Pa.g;var a=this.Pa.h;this.tb=p(33,this.tb)+a|0;this.tb=p(17,this.tb)+this.x|0}else this.tb=p(17,this.Jd.z())+this.x|0;return this.tb};e.Rb=function(){return-32>=this.x||this.x>Tn(this)?0:Un(this).Rb()};e.Fe=function(a){ql.prototype.li.call(this,a,0);return this};
e.De=function(){var a=this.Va,b=a>>31,c=x(),d=tj(c,this.x/.3010299956639812);c=c.v;d=a-d|0;a=(-2147483648^d)>(-2147483648^a)?-1+(b-c|0)|0:b-c|0;b=da(io(this));return(-1===a?2147483499>(-2147483648^d):-1>a)||0===b?da(0*b):(0===a?-2147483519<(-2147483648^d):0<a)?da(Infinity*b):da(this.gd())};
e.Qp=function(a,b){ql.prototype.a.call(this);var c=-1+(0+b|0)|0;if(null===a)throw(new si).k("in \x3d\x3d null");if(c>=a.c.length||0>=b||0>c)throw(new Sl).k("Bad offset/length: offset\x3d0 len\x3d"+b+" in.length\x3d"+a.c.length);var d=0;if(0<=c&&43===a.c[0]){d=1+d|0;if(d<c){X();for(var f=[Fl(43),Fl(45)],g=Fl(a.c[d]),h=0;;){if(h<(f.length|0))var k=f[h],m=!1===T(U(),k,g);else m=!1;if(m)h=1+h|0;else break}var n=h!==(f.length|0)}else n=!1;if(n)throw(new Sl).k("For input string: "+a.r());}else{var q=d<=
c&&45===a.c[d];if((1+d|0)<c){X();for(var r=[Fl(43),Fl(45)],w=Fl(a.c[1+d|0]),A=0;;){if(A<(r.length|0))var E=r[A],I=!1===T(U(),E,w);else I=!1;if(I)A=1+A|0;else break}var P=A!==(r.length|0)}else P=!1;if(q&&P)throw(new Sl).k("For input string: "+a.r());}for(var oa=d,ba=!1;;){if(d<=c){X();for(var la=[Fl(46),Fl(101),Fl(69)],cd=Fl(a.c[d]),za=0;;){if(za<(la.length|0))var dd=la[za],ni=!1===T(U(),dd,cd);else ni=!1;if(ni)za=1+za|0;else break}var Ds=za===(la.length|0)}else Ds=!1;if(Ds)ba||48===a.c[d]||(ba=!0),
d=1+d|0;else break}var Es=Ci(Ga(),a,oa,d-oa|0),Fs=d-oa|0;if(d<=c&&46===a.c[d]){for(var Gs=d=1+d|0;;){if(d<=c){X();for(var yo=[Fl(101),Fl(69)],dv=Fl(a.c[d]),gj=0;;){if(gj<(yo.length|0))var ev=yo[gj],Hs=!1===T(U(),ev,dv);else Hs=!1;if(Hs)gj=1+gj|0;else break}var Is=gj===(yo.length|0)}else Is=!1;if(Is)ba||48===a.c[d]||(ba=!0),d=1+d|0;else break}this.x=d-Gs|0;Ga();var Js=""+Es+Ci(0,a,Gs,this.x),Ks=Fs+this.x|0}else this.x=0,Js=Es,Ks=Fs;var Ra=Js,fv=Ks|0;if(d<=c){X();for(var zo=[Fl(101),Fl(69)],gv=Fl(a.c[d]),
hj=0;;){if(hj<(zo.length|0))var hv=zo[hj],Ls=!1===T(U(),hv,gv);else Ls=!1;if(Ls)hj=1+hj|0;else break}var Ms=hj!==(zo.length|0)}else Ms=!1;if(Ms){d=1+d|0;var iv=(1+d|0)<=c&&45!==a.c[1+d|0],Ns=d<=c&&43===a.c[d]&&iv?1+d|0:d,jv=Ci(Ga(),a,Ns,(1+c|0)-Ns|0),Ao=this.x,Os=Ao>>31,Ps=vc(wc(),jv,10),Qs=Ps>>31,Bo=Ao-Ps|0,Rs=this.x=Bo;if(Bo!==Rs||((-2147483648^Bo)>(-2147483648^Ao)?-1+(Os-Qs|0)|0:Os-Qs|0)!==Rs>>31)throw(new Sl).k("Scale out of range");}if(19>fv){hm||(hm=(new em).a());var ij=hm;""===Ra&&fm(Ra);var Co=
0,Ss=!1;switch(65535&(Ra.charCodeAt(0)|0)){case 43:Co=1;break;case 45:Co=1,Ss=!0}var Ts=Co,Md=Ra.length|0;if(Ts>=Md){fm(Ra);var jj=void 0}else{if(!ij.t&&!ij.t){for(var Do=[],Zb=0;2>Zb;)Do.push(null),Zb=1+Zb|0;for(;36>=Zb;){for(var kv=2147483647/Zb|0,Jl=Zb,Eo=1;Jl<=kv;)Jl=p(Jl,Zb),Eo=1+Eo|0;var Fo=Jl,Us=Fo>>31,Vs=x(),lv=Ye(Vs,-1,-1,Fo,Us),mv=Vs.v,Kl=new Hf,nv=(new v).f(Fo,Us),ov=(new v).f(lv,mv);Kl.qj=Eo;Kl.Dk=nv;Kl.xk=ov;Do.push(Kl);Zb=1+Zb|0}ij.lj=Do;ij.t=!0}for(var Go=ij.lj[10],Ho=Go.qj,Ac=Ts;;){var Io;
if(Io=Ac<Md){var pv=Ql(),Jo=65535&(Ra.charCodeAt(Ac)|0);Io=256>Jo?48===Jo:0<=Mf(Of(),Il(pv),Jo)}if(Io)Ac=1+Ac|0;else break}(Md-Ac|0)>p(3,Ho)&&fm(Ra);var Ll=Ac+(1+((-1+(Md-Ac|0)|0)%Ho|0)|0)|0,Ml=gm(Ac,Ll,Ra);if(Ll===Md)jj=(new v).f(Ml,0);else{var Ws=Go.Dk,kj=Ws.g,Xs=Ws.h,Ko=Ll+Ho|0,Ys=65535&Ml,Zs=Ml>>>16|0,$s=65535&kj,at=kj>>>16|0,bt=p(Ys,$s),ct=p(Zs,$s),dt=p(Ys,at),et=bt+((ct+dt|0)<<16)|0,ft=(bt>>>16|0)+dt|0,gt=((p(Ml,Xs)+p(Zs,at)|0)+(ft>>>16|0)|0)+(((65535&ft)+ct|0)>>>16|0)|0,qv=gm(Ll,Ko,Ra),fh=
et+qv|0,Nl=(-2147483648^fh)<(-2147483648^et)?1+gt|0:gt;if(Ko===Md)jj=(new v).f(fh,Nl);else{var ht=Go.xk,rv=ht.g,it=ht.h,jt=gm(Ko,Md,Ra);(Nl===it?(-2147483648^fh)>(-2147483648^rv):Nl>it)&&fm(Ra);var kt=65535&fh,lt=fh>>>16|0,mt=65535&kj,nt=kj>>>16|0,ot=p(kt,mt),pt=p(lt,mt),qt=p(kt,nt),rt=ot+((pt+qt|0)<<16)|0,st=(ot>>>16|0)+qt|0,tt=(((p(fh,Xs)+p(Nl,kj)|0)+p(lt,nt)|0)+(st>>>16|0)|0)+(((65535&st)+pt|0)>>>16|0)|0,Lo=rt+jt|0,ut=(-2147483648^Lo)<(-2147483648^rt)?1+tt|0:tt;-2147483648===(-2147483648^ut)&&
(-2147483648^Lo)<(-2147483648^jt)&&fm(Ra);jj=(new v).f(Lo,ut)}}}var Mo=jj.g,Ol=jj.h;if(Ss){var vt=-Mo|0,No=0!==Mo?~Ol:-Ol|0;(0===No?0!==vt:0<No)&&fm(Ra);var wt=(new v).f(vt,No)}else 0>Ol&&fm(Ra),wt=(new v).f(Mo,Ol);this.Pa=wt;this.Va=tl(X(),this.Pa)}else ho(this,(new S).k(Ra))};function Zn(a){null===a.Jd&&(a.Jd=lf(R(),a.Pa));return a.Jd}
function lo(a,b){var c=io(a),d=io(b);if(c===d){if(a.x===b.x&&64>a.Va&&64>b.Va){c=a.Pa;d=c.g;c=c.h;var f=b.Pa,g=f.h;if(c===g?(-2147483648^d)<(-2147483648^f.g):c<g)return-1;d=a.Pa;a=d.g;d=d.h;b=b.Pa;c=b.h;return(d===c?(-2147483648^a)>(-2147483648^b.g):d>c)?1:0}f=a.x;g=f>>31;d=b.x;var h=d>>31;d=f-d|0;f=(-2147483648^d)>(-2147483648^f)?-1+(g-h|0)|0:g-h|0;g=Tn(a)-Tn(b)|0;h=g>>31;var k=1+d|0,m=0===k?1+f|0:f;if(h===m?(-2147483648^g)>(-2147483648^k):h>m)return c;h=g>>31;k=-1+d|0;m=-1!==k?f:-1+f|0;if(h===m?
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