#pragma region template #pragma GCC optimize("Ofast") #include using namespace std; #ifdef __LOCAL #include #else #define debug(...) void(0) #endif using ll=long long; using ld=long double; using vi=vector; using vll=vector; using pi=pair; using pll=pair; #define overload2(a,b,c,...) c #define overload3(a,b,c,d,...) d #define overload4(a,b,c,d,e,...) e #define overload5(a,b,c,d,e,f,...) f #define TYPE1(T) template #define TYPE2(T,U) template #define TYPE(...) overload2(__VA_ARGS__,TYPE2,TYPE1)(__VA_ARGS__) #define TYPES1(T) template #define TYPES2(H,T) template #define TYPES(...) overload2(__VA_ARGS__,TYPES2,TYPES1)(__VA_ARGS__) #define REP4(i,s,n,d) for(int i=(s);i<(n);i+=(d)) #define REP3(i,s,n) REP4(i,s,n,1) #define REP2(i,n) REP3(i,0,n) #define REP1(n) REP2(tomato,n) #define REP(...) overload4(__VA_ARGS__,REP4,REP3,REP2,REP1)(__VA_ARGS__) #define RREP4(i,n,s,d) for(int i=(n)-1;i>=s;i-=d) #define RREP3(i,n,s) RREP4(i,n,s,1) #define RREP2(i,n) RREP3(i,n,0) #define RREP1(n) RREP2(tomato,n) #define RREP(...) overload4(__VA_ARGS__,RREP4,RREP3,RREP2,RREP1)(__VA_ARGS__) #define FOR4(a,b,c,d,v) for(auto [a,b,c,d]:v) #define FOR3(a,b,c,v) for(auto [a,b,c]:v) #define FOR2(a,b,v) for(auto [a,b]:v) #define FOR1(a,v) for(auto a:v) #define FOR(...) overload5(__VA_ARGS__,FOR4,FOR3,FOR2,FOR1)(__VA_ARGS__) #define AFOR4(a,b,c,d,v) for(auto&[a,b,c,d]:v) #define AFOR3(a,b,c,v) for(auto&[a,b,c]:v) #define AFOR2(a,b,v) for(auto&[a,b]:v) #define AFOR1(a,v) for(auto&a:v) #define AFOR(...) overload5(__VA_ARGS__,AFOR4,AFOR3,AFOR2,AFOR1)(__VA_ARGS__) #define CFOR4(a,b,c,d,v) for(const auto&[a,b,c,d]:v) #define CFOR3(a,b,c,v) for(const auto&[a,b,c]:v) #define CFOR2(a,b,v) for(const auto&[a,b]:v) #define CFOR1(a,v) for(const auto&a:v) #define CFOR(...) overload5(__VA_ARGS__,CFOR4,CFOR3,CFOR2,CFOR1)(__VA_ARGS__) #define ALL(v) v.begin(),v.end() #define RALL(v) v.rbegin(),v.rend() #define SORT(v) sort(ALL(v)) #define RSORT(v) sort(RALL(v)) #define REVERSE(v) reverse(ALL(v)) #define UNIQUE(v) SORT(v),v.erase(unique(ALL(v)),v.end()) TYPES(T) void input(T&... a){ (cin>>...>>a); } #define DECLARE(T,...) T __VA_ARGS__;input(__VA_ARGS__); #define INT(...) DECLARE(int,__VA_ARGS__) #define STR(...) DECLARE(string,__VA_ARGS__) #define LL(...) DECLARE(long long,__VA_ARGS__) #define CHR(...) DECLARE(char,__VA_ARGS__) #define DBL(...) DECLARE(double,__VA_ARGS__) #define VI(n,v) vi v(n);cin>>v; #define VLL(n,v) vll v(n);cin>>v; TYPE(T) istream&operator>>(istream&is,vector&v){ for(auto&a:v)cin>>a; return is; } TYPE(T) ostream&operator<<(ostream&os,const vector&v){ if(&os==&cerr)os<<"["; REP(i,v.size()){ os<>(istream&is,pair&p){ cin>>p.first>>p.second; return is; } void print(){ cout << '\n'; } TYPES(T,Ts) void print(const T& a,const Ts&... b){ cout<; TYPE(T) using pqg=priority_queue,greater>; TYPE(T) T pick(queue& que){assert(que.size()); T a=que.front();que.pop();return a;} TYPE(T) T pick(pq& que){assert(que.size()); T a=que.top();que.pop();return a;} TYPE(T) T pick(pqg& que){assert(que.size()); T a=que.top();que.pop();return a;} TYPE(T) T pick(stack& sta){assert(sta.size()); T a=sta.top();sta.pop();return a;} string YES(bool f=true){return (f?"YES":"NO");} string Yes(bool f=true){return (f?"Yes":"No");} string yes(bool f=true){return (f?"yes":"no");} constexpr int INF=1e9+7; constexpr ll LINF=ll(1e18)+7; constexpr ld EPS=1e-10; vi iota(int n){vi a(n);iota(ALL(a),0);return a;} TYPE(T) T rev(T a){ REVERSE(a);return a; } TYPE(T) void fin(T a){cout<b&&(a=b,true));} TYPES(T,Ns) auto make_vector(T x,int n,Ns ...ns){ if constexpr(sizeof...(ns)==0)return vector(n,x); else return vector(n,make_vector(x,ns...)); } bool in(const ll S,const int a){return (S>>a)&1;} int popcount(const ll S){return __builtin_popcountll(S);} #pragma endregion template template class Doubling{ using X=typename Monoid::value_type; int n; bool is_prepared; using P=pair; static constexpr P unit={-1,Monoid::unit()}; vector> DP; P k_move(const P&a,int k){ if(a.first==-1)return a; const auto [now,val]=a; const auto [nxt,cost]=DP[k][now]; return {nxt,Monoid::op(val,cost)}; } void build(){ is_prepared=true; for(int k=0;k(n,unit)); } void add_arc(int from,int to,X x){ assert(!is_prepared); assert(-1<=to and to>=1) if(step&1)res=k_move(res,k); return res; } }; template struct Group_Add { using value_type = X; static constexpr X op(const X &x, const X &y) noexcept { return x + y; } static constexpr X inverse(const X &x) noexcept { return -x; } static constexpr X power(const X &x, long long n) noexcept { return X(n) * x; } static constexpr X unit() { return X(0); } static constexpr bool commute = true; }; using G=Group_Add; const ll MOD=1000000000; int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); INT(s); LL(m,l); Doubling db(10000); auto F=[](ll &a,ll &b,ll &c,ll A,ll B,ll C,ll D){ ll na= a*A + b*B%MOD*D; ll nb= a*B+b*A; c+=C; while( na%2==0 and nb%2==0 and c>0){ na/=2; nb/=2; c--; } na%=MOD;nb%=MOD; a=na; b=nb; }; REP(n,10000){ int D=n*n+4; ll A=n,B=1,C=1; ll X=m; ll a=1,b=0,c=0; if(~n&1){ A=n/2; C=0; D=n*n/4+1; c=1; } while(X){ if(X&1)F(a,b,c,A,B,C,D); F(A,B,C,A,B,C,D); X>>=1; } ld y=a+b*sqrt(D); y/=pow(2,c); if(n==1020)debug(y); y/=sqrt(D); if(n==10||n==1020)debug(n,y); ll to=round(y);if(n==10||n==1020)debug(n,to); to%=10000; if(n==10||n==1020)debug(n,to); db.add_arc(n,to,0); } int ans=db.calc(s,l).first; string fans=to_string(ans); while(fans.size()<4)fans="0"+fans; fin(fans); }