#if __has_include() #include using namespace atcoder; using mint=modint998244353; using mint1=modint1000000007; #endif #if __has_include() && __has_include() #include #include using namespace __gnu_pbds; templateusing __gnu_map=tree,rb_tree_tag,tree_order_statistics_node_update>; templatestruct gnu_map:public __gnu_map{ using iterator=typename __gnu_map::iterator; iterator get(int64_t idx){return this->find_by_order(idx<0?this->size()-idx:idx);} size_t ord(const s&key){return this->order_of_key(key);} }; templatestruct gnu_set:public gnu_map{gnu_map::iterator operator[](int64_t i){return this->get(i);}}; #endif #include using namespace std; using std::cin; using std::cout; using sstream=stringstream; #define RET return #define int long long #define itn long long #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 elif(c) else if(c) #define _SEL4(_1,_2,_3,_4,name,...) name #define _SEL3(_1,_2,_3,name,...) name #define _REP4(i,s,n,st) for(int 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(int 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 forif(c,...) rep(__VA_ARGS__)if(c) #define iter(...) _SEL3(__VA_ARGS__,_ITER3,_ITER2)(__VA_ARGS__) #define cter(...) _SEL3(__VA_ARGS__,_CTER3,_CTER2)(__VA_ARGS__) #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(...) _SEL4(__VA_ARGS__,_LB_BEXG,_LB_BEX)(__VA_ARGS__) #define ub(...) _SEL4(__VA_ARGS__,_UB_BEXG,_UB_BEX)(__VA_ARGS__) #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) #define NL cout<<'\n' templateusing gr=greater; templateusing vc=vector; templateusing vv=vc>; templateusing v3=vv>; templateusing v4=vv>; templateusing pq=priority_queue; templateusing pqg=priority_queue, gr>; #define uset unordered_set #define umap unordered_map using i8=int8_t; using i16=int16_t; using i32=int32_t; using i64=int64_t; using i128=__int128_t; using u8=uint8_t;using u16=uint16_t;using u32=uint32_t;using u64=uint64_t;using u128=__uint128_t; using intw=__int128_t;using uintw=__uint128_t; using it=i32; using f32=float;using f64=double;using f128=long double; using vi=vc;using vb=vc; using pi=pair; using str=string;using vs=vc; using pqgp=pqg; #define double f128 constexpr int inf=1ll<<60,minf=-inf; constexpr char sep='\n'; constexpr arraydc={{{1,0},{0,1},{-1,0},{0,-1},{1,1},{1,-1},{-1,1},{-1,-1}}}; templateinline void chmax(T&a,const U&b){if(ainline void chmin(T&a,const U&b){if(a>b)a=b;} #define yes cout<<"Yes\n" #define no cout<<"No\n" #define yn(c) (c)?yes:no #if __cplusplus <= 202002L #else #define C const 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 INT(...) int __VA_ARGS__;getv(__VA_ARGS__) #define CHR(...) char __VA_ARGS__;getv(__VA_ARGS__) #define STR(...) str __VA_ARGS__;getv(__VA_ARGS__) #define VI(a,n) vi a(n);getv(a) #define VS(a,n) vs a(n);getv(a) #define UV(u,v) INT(u,v);u--,v-- #define UVW(u,v,w) INT(u,v,w);u--,v-- templateinline auto ceil(C T a,C U b){return(a+b-1)/b;} templateinline auto floor(C T a,C U b){return a/b-(a%b&&(a^b)<0);} templateconcept LUBI= same_as>||same_as>||is_array_v; #define TP template> #define RL requires LUBI TP u64 lbi(C T&v,C U&x,cp cmp=cp())RL{RET lb(A(v),x,cmp)-begin(v);} TP u64 ubi(C T&v,C U&x,cp cmp=cp())RL{RET ub(A(v),x,cmp)-begin(v);} TP u64 lbi(u64 i,C T&v,C U&x,cp cmp=cp())RL{RET lb(i+A(v),x,cmp)-begin(v);} TP u64 ubi(u64 i,C T&v,C U&x,cp cmp=cp())RL{RET ub(i+A(v),x,cmp)-begin(v);} TP u64 lbi(C T&v,u64 i,C U&x,cp cmp=cp())RL{RET lb(I(v,i),x,cmp)-begin(v);} TP u64 ubi(C T&v,u64 i,C U&x,cp cmp=cp())RL{RET ub(I(v,i),x,cmp)-begin(v);} TP u64 lbi(u64 i,C T&v,u64 e,C U&x,cp cmp=cp())RL{RET lb(i+I(v,e),x,cmp)-begin(v);} TP u64 ubi(u64 i,C T&v,u64 e,C U&x,cp cmp=cp())RL{RET ub(i+I(v,e),x,cmp)-begin(v);} #undef TP #undef RL #define TP template TPconcept Lint=is_integral_v&&sizeof(T)>8; TPostream&operator<<(ostream&dst,T val){ ostream::sentry s(dst); if(!s)return dst; char _O128[64]; char*d=end(_O128); bool vsign=val<0; uintw v=val; if(vsign&&val!=numeric_limits::min())v=1+~(uintw)val; do{ *(--d)="0123456789"[v%10]; v/=10; }while(v!=0); if(vsign)*(--d)='-'; size_t len=end(_O128)-d; if(dst.rdbuf()->sputn(d,len)!=len)dst.setstate(ios_base::badbit); return dst; } TPistream&operator>>(istream&src,T&val) { str s;src>>s; bool is_neg=numeric_limits::is_signed&&s.size()>0&&s[0]=='-'; for(val=0;C auto&x:s|views::drop(is_neg))val=10*val+x-'0'; if(is_neg)val*=-1; return src; } #define MUT make_unsigned_t TPi32 pcnt(T p){return popcount(MUT(p));} TPi32 lsb(T p){return countl_zero(MUT(p));} TPi32 msb(T p){return countr_zero(MUT(p));} TPconcept Itrabl=requires(C T&x){x.begin();x.end();}; TPconcept IItrabl=Itrabl&&Itrabl; TPconcept ModInt=requires(C T&x){x.val();}; void _getv(str&a){cin>>a;} TPvoid _getv(T&a){cin>>a;} TPvoid _getv(pair&a){_getv(a.fi);_getv(a.se);} TPvoid _getv(T&a){iter(x,a)_getv(x);} TPvoid getv(T&a){_getv(a);} TPvoid getv(T&a,Ts&... b){_getv(a);getv(b...);} ostream*dos=&cout; void _putv(C str&a){(*dos)<void _putv(C T&a){(*dos)<void _putv(C pair&a){_putv(a.fi);_putv(a.se);} TPvoid _putv(C T&a){_putv(a.val());} TPvoid _putv(C T&a){cter(x,a)_putv(x);(*dos)<void _putv(C T&a){cter(y,a)_putv(y);} TPvoid _putv(C T&a)requires same_as{cter(x,a)_putv(x);} TPvoid putv(C T&a){_putv(a);(*dos)<void putv(C T&a,C Ts&... b){_putv(a);putv(b...);} TP void putbit(T s,char sep='\n'){ char buf[N+1]={0}; for(char*itr=buf+N-1;itr>=buf;itr--,s>>=1) *itr='0'+(s&1); cout< T exgcd(T a,T b,T&x,T&y){ auto eq=[](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; eq(x,u,u,x-k*u); eq(y,v,v,y-k*v); eq(a,b,b,a%b); }return a; } template paircrt(const vector&b,const vector&m){ T r=0,M=1; for(size_t i=0;i b(3),m(3); rep(i,3)getv(b[i],m[i]); auto [p,k]=::crt(b,m); if(p==0&&k==-1)cout<<-1<sync_with_stdio(0); cout<