#ifndef ELSIE_LOCAL_H #define ELSIE_LOCAL_H #ifndef ELSIE_MISC_HEADER #define ELSIE_MISC_HEADER #if __has_include() #include "atcoder/modint" using namespace atcoder; using mint=modint998244353; using mint1=modint1000000007; #endif #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using namespace chrono; using std::cin; using std::cout; using sstream=stringstream; #endif #ifndef ELSIE_MISC_DEFINE #define ELSIE_MISC_DEFINE #define RET return #define fi first #define se second #define endl '\n' #define sn(i,c) " \n"[i==c] #define rsv(n) reserve(n) #define pf(a) push_front(a) #define pb(a) push_back(a) #define eb(...) emplace_back(__VA_ARGS__) #define ppf() pop_front() #define ppb() pop_back() #define pp() pop() #define ins(a) insert(a) #define emp(...) emplace(__VA_ARGS__) #define ers(a) erase(a) #define cont(a) contains(a) #define mp(f,s) make_pair(f,s) #define A(a) begin(a),end(a) #define I(a,i) begin(a),begin(a)+(i) #define _SEL4(_1,_2,_3,_4,name,...) name #define _SEL3(_1,_2,_3,name,...) name #define _REP4(i,s,n,st) for(long i=(s);i<(n);i+=(st)) #define _REP3(i,s,n) _REP4(i,s,n,1) #define _REP2(i,n) _REP3(i,0,n) #define _REP1(n) _REP2(_,n) #define _RREP4(i,n,t,s) for(long i=(n);i>=(t);i-=(s)) #define _RREP3(i,n,t) _RREP4(i,n,t,1) #define _RREP2(i,n) _RREP3(i,n,0) #define _ITER2(x,a) for(auto&&x:a) #define _ITER3(x,y,a) for(auto&&[x,y]:a) #define _CTER2(x,a) for(const auto&x:a) #define _CTER3(x,y,a) for(const auto&[x,y]:a) #define rep(...) _SEL4(__VA_ARGS__,_REP4,_REP3,_REP2,_REP1)(__VA_ARGS__) #define rrep(...) _SEL4(__VA_ARGS__,_RREP4,_RREP3,_RREP2,_REP1)(__VA_ARGS__) #define iter(...) _SEL3(__VA_ARGS__,_ITER3,_ITER2)(__VA_ARGS__) #define cter(...) _SEL3(__VA_ARGS__,_CTER3,_CTER2)(__VA_ARGS__) #endif #ifndef ELSIE_MISC_CONST #define ELSIE_MISC_CONST #define NL cout<<'\n' #define npi numbers::pi constexpr int64_t inf=1ll<<60,minf=-inf; constexpr int32_t inf32=1ll<<30,minf32=-inf32; constexpr char sep='\n'; constexpr array,8>dc={{{1,0},{0,1},{-1,0},{0,-1},{1,1},{1,-1},{-1,1},{-1,-1}}}; #define yes cout<<"Yes\n" #define no cout<<"No\n" #define yn(c) (c)?yes:no #endif #if __cplusplus > 202002L #ifndef ELSIE_MISC_FUNC #define ELSIE_MISC_FUNC namespace vies=std::views; #define DR(i) views::drop(i) #define TK(i) views::take(i) #define RV views::reverse #define IOTA vies::iota #define rev(a) reverse(A(a)) #define minel(a) min_element(A(a)) #define maxel(a) max_element(A(a)) #define acm(a) accumulate(A(a),0ll) #define nxpm(a) next_permutation(A(a)) #define Sort(a) sort(A(a)) #define uni(a) Sort(a);a.erase(unique(A(a)),a.end()) #define swapcase(a) a=(isalpha(a)?a^32:a) templateinline void chmax(T&a,const U&b){if(ainline void chmin(T&a,const U&b){if(a>b)a=b;} #define _BISECT4(_1,_2,_3,_4,name,...) name #define _LB_BEX(b,e,x) lower_bound(b,e,x) #define _LB_BEXG(b,e,x,g) lower_bound(b,e,x,g) #define _UB_BEX(b,e,x) upper_bound(b,e,x) #define _UB_BEXG(b,e,x,g) upper_bound(b,e,x,g) #define lb(...) _BISECT4(__VA_ARGS__,_LB_BEXG,_LB_BEX)(__VA_ARGS__) #define ub(...) _BISECT4(__VA_ARGS__,_UB_BEXG,_UB_BEX)(__VA_ARGS__) #define TP template> templateconcept LUBI= same_as>||same_as>||is_array_v; #define RL requires LUBI TP size_t lbi(const T&v,const U&x,cp cmp=cp())RL{RET lb(A(v),x,cmp)-begin(v);} TP size_t ubi(const T&v,const U&x,cp cmp=cp())RL{RET ub(A(v),x,cmp)-begin(v);} TP size_t lbi(size_t i,const T&v,const U&x,cp cmp=cp())RL{RET lb(i+A(v),x,cmp)-begin(v);} TP size_t ubi(size_t i,const T&v,const U&x,cp cmp=cp())RL{RET ub(i+A(v),x,cmp)-begin(v);} TP size_t lbi(const T&v,size_t i,const U&x,cp cmp=cp())RL{RET lb(I(v,i),x,cmp)-begin(v);} TP size_t ubi(const T&v,size_t i,const U&x,cp cmp=cp())RL{RET ub(I(v,i),x,cmp)-begin(v);} TP size_t lbi(size_t i,const T&v,size_t e,const U&x,cp cmp=cp())RL{RET lb(i+I(v,e),x,cmp)-begin(v);} TP size_t ubi(size_t i,const T&v,size_t e,const U&x,cp cmp=cp())RL{RET ub(i+I(v,e),x,cmp)-begin(v);} #undef TP #undef RL #define TP template #define MT make_unsigned_t TP constexpr int32_t pcnt(T p){return popcount(MT(p));} TP constexpr int32_t lsb(T p){return countr_zero(MT(p));} TP constexpr int32_t msb(T p){return sizeof(T)*8-1-countl_zero(MT(p));} template void putbit(T s){ char buf[N+1]={0}; for(char*itr=buf+N-1;itr>=buf;itr--,s>>=1) *itr='0'+(s&1); cout<concept Lint=same_as||same_as; templateconcept Itrabl=requires(const T&x){x.begin();x.end();}&&!std::is_same_v; templateconcept IItrabl=Itrabl&&Itrabl; templateconcept ModInt=requires(const T&x){x.val();}; templateconcept NLobj=Itrabl||std::is_same_v; istream&operator<<(istream&is,__float128&x){double y;is>>y;x=y;return is;} ostream&operator<<(ostream&os,const __float128&x){return os<(x);} templateostream&operator<<(ostream&dst,T val){ ostream::sentry s(dst); if(!s)return dst; char _O128[64]; char*d=end(_O128); bool vsign=val<0; __uint128_t v=val; if(vsign&&val!=numeric_limits::min())v=1+~(__uint128_t)val; do{ *(--d)="0123456789"[v%10]; v/=10; }while(v!=0); if(vsign)*(--d)='-'; ptrdiff_t len=end(_O128)-d; if(dst.rdbuf()->sputn(d,len)!=len)dst.setstate(ios_base::badbit); return dst; } templateistream&operator>>(istream&src,T&val) { string s;src>>s; bool is_neg=numeric_limits::is_signed&&s.size()>0&&s[0]=='-'; for(val=0;const auto&x:s|views::drop(is_neg))val=10*val+x-'0'; if(is_neg)val*=-1; return src; } templateistream&operator>>(istream&is,T&v){int64_t x;is>>x;v=x;return is;} templateistream&operator>>(istream&is,pair&v){return is>>v.first>>v.second;} templateistream&operator>>(istream&is,T&v){for(auto&&x:v)is>>x;return is;} templatevoid in(T&a){cin>>a;} templatevoid in(T&a,Ts&... b){in(a);in(b...);} templatevector>zip(size_t n,size_t m){ vector>r(min(n,m)); iter(x,y,r)in(x); iter(x,y,r)in(y); return move(r); } templatevector>zip(size_t n){return move(zip(n,n));} templateostream&operator<<(ostream&os,const T&v){return os<ostream&operator<<(ostream&os,const pair&v){return os<<'('<ostream&operator<<(ostream&os,const T&v){size_t cnt=0;cter(x,v)os<ostream&operator<<(ostream&os,const T&v){size_t cnt=0;cter(x,v)os<void _out(const T&a){if(OFLG)(*dos)<<"0 \n"[OFLG]<void _out(const T&a){(*dos)<<(OFLG?"\n":"")<void _out(const T&a,const Ts&... b){_out(a);_out(b...);} templatevoid out(const Ts&... v){OFLG=0;_out(v...);(*dos)< inline auto ceil(const T a,const U b){return(a+b-1)/b;} template inline auto floor(const T a,const U b){return a/b-(a%b&&(a^b)<0);} // std::ceil(std::sqrtl(x:u64))が64bit精度で40%高速なので,long double 80bitならそちらを使うべき template inline uint64_t sqrt_ceil(uint64_t x){ if constexpr(!internal_invocate){ // sqrt_floorからの呼出しではここをスキップする if(x>uint64_t(UINT32_MAX)*UINT32_MAX)return 1ull<<32; else if(x<2)return x!=0; } uint64_t nx,y=min((1ULL<<((64-countl_zero(x))>>1)+1)-1,UINT32_MAX); y-=(y*y-x)/(y<<1); y-=(y*y-x)/(y<<1); y-=(y*y-x)/(y<<1); y-=(y*y-x)/(y<<1); y-=(y*y-x)/(y<<1); nx=y-(y*y-x)/(y<<1); while(nx!=y){ y=nx; nx=y-(y*y-x)/(y<<1); if(nx==y)break; } return y+(y*y=x?-1:0); } inline uint64_t sqrt_floor(uint64_t x){ if((uint64_t)UINT32_MAX*UINT32_MAX<=x)return UINT32_MAX; else if(x<4)return x!=0; uint64_t y=sqrt_ceil(x); return y-(y*y!=x); } using u128=__uint128_t; using u64 = uint64_t; inline __uint128_t mul64to128(u64 a,u64 b){ u64 hi,lo; asm("mulq %3" :"=a"(lo),"=d"(hi):"a"(a),"r"(b)); return((__uint128_t)(hi)<<64)+lo; } inline pairmul128(u128 a,u128 b){ constexpr static u128 Lfilter=0xFFFF'FFFF'FFFF'FFFFull; u64 x1=a>>64,x0=a&Lfilter; u64 y1=b>>64,y0=b&Lfilter; u128 z2=mul64to128(x1,y1),z1=mul64to128(x1,y0)+mul64to128(x0,y1),z0=mul64to128(x0,y0); u128 lower=z0+(z1<<64); return{z2+(z1>>64)+(lowerx,u128 mod){ u128 rem32=(u128(1)<<32)%mod; u128 rem64=rem32*rem32%mod; u128 rem128=rem64*rem64%mod; auto&&[a,b]=x; a%=mod,b%=mod; return(a*rem128%mod+b)%mod; } int64_t safepow(int64_t a,uint64_t b){ int64_t ret=1,k=a; double check=1,kcheck=a; while(b){ if(b&1){ check*=k; if(check>INT64_MAX)return INT64_MAX; if(checkINT64_MAX)return INT64_MAX; if(kcheck>=1; } return ret; } template> constexpr T modpow(T a,U b,U mod){ if constexpr(is_same_v){ // mod=2^64専用 constexpr __uint128_t filter=uint64_t(-1); a%=mod; __uint128_t ret=1; if(a<0)a+=mod; while(b){ ret=(b&1?ret*a&filter:ret); a=a*a&filter; b>>=1; } return uint64_t(ret&filter); }else{ __int128_t k=a%mod,ret=1; if(k<0)k+=mod; while(b){ ret=(b&1?ret*k%mod:ret); k=(k*k)%mod; b>>=1; } return int64_t(ret); } } templateS gcd(S a,S b){ if(b==0) return a; S r=1;if(a<0)a=-a;if(b<0)b=-b; while(r) r=a%b,a=b,b=r; return a; } templateS lcm(S a,S b){return a/gcd(a,b)*b;} templateS egcd(S a,S b,S&x,S&y){ if(b==0){ x=1,y=0; return a; } S d=egcd(b,a%b,y,x); y-=a/b*x; return d; } templateT exgcd(T a,T b,T&x,T&y){ auto assign=[&](T&s,T&t,T u,T v)->void {s=u,t=v;}; x=1,y=0; T u=0,v=1; while(b){ T k=a/b,r=a%b; assign(a,b,b,r); assign(x,u,u,x-u*k); assign(y,v,v,y-v*k); } if constexpr(is_signed_v) if(a<0)a=-a,x=-x,y=-y; return a; } templateT mod_inv(T a,T m){ T x,y,g=exgcd(a,m,x,y); if(g!=1)return -1; return(x%m+m)%m; } templateT mod_inv_prime(T a,T p){ return modpow(a,p-2,p); } template class combination{ private: using tint = long long; vectorinvprod,prod; vectorinv; const unsigned long long M; public: combination(int64_t n=1):invprod(2,1),prod(2,1),inv(2,0),M(mint(-1).val()+1){ inv[1]=1; if(n>1)PreCalc(n); } void PreCalc(int64_t n){ size_t presize=inv.size(); if(presize>=n+1)return; inv.resize(n+1); prod.resize(n+1); invprod.resize(n+1); for(int64_t i=presize;i<=n;++i){ prod[i]=prod[i-1]*i; inv[i]=(((M/i)*(-inv[M%i]))+M)%M; invprod[i]=invprod[i-1]*inv[i]; } } mint factorial(size_t n){ PreCalc(n); return prod[n]; } mint invfact(size_t n){ PreCalc(n); return invprod[n]; } mint P(size_t n,size_t k){ if(n>64); uint64_t y=x*M; return(uint32_t)(z-y+(zusing vc=vector; templateusing vv=vc>; templateusing v3=vv>; templateusing v4=vv>; templateusing gr=greater; templateusing pq=priority_queue; templateusing pqg=priority_queue, gr>; #define uset unordered_set #define umap unordered_map using it=int32_t; using i8=int8_t; using u8=uint8_t; using i16=int16_t; using u16=uint16_t; using i32=int32_t; using u32=uint32_t; using i64=int64_t; using u64=uint64_t; using i128=__int128_t; using u128=__uint128_t; using intw=__int128_t; using uintw=__uint128_t; using f32=float; using f64=double; using f128=__float128; using vi=vc; using vit=vc; using vb=vc; using pi=pair; using pit=pair; using str=string; using vs=vc; using pqgp=pqg; #define int i64 #define itn i64 #define LL long long #endif void slv(){ constexpr int s=1'000'000'000; INT(n,m); n%=s; m%=s; if(m)m=s-m; if(n==0){ if(m%s)out(-1); else out(1); return; } int k=elsie::mod_inv(n,s); if(k==-1&&m%n!=0) out(-1); else if(k!=-1)out(m*k); else out(m/n); } signed main(){ cin.tie(0)->sync_with_stdio(0); cout<