#include using namespace std; using ll=long long; #define int ll #define rng(i,a,b) for(int i=int(a);i=int(a);i--) #define per(i,b) gnr(i,0,b) #define pb push_back #define eb emplace_back #define a first #define b second #define bg begin() #define ed end() #define all(x) x.bg,x.ed #define si(x) int(x.size()) #ifdef LOCAL #define dmp(x) cerr<<__LINE__<<" "<<#x<<" "< void chmax(t&a,u b){if(a void chmin(t&a,u b){if(b using vc=vector; template using vvc=vc>; using pi=pair; using vi=vc; template ostream& operator<<(ostream& os,const pair& p){ return os<<"{"< ostream& operator<<(ostream& os,const vc& v){ os<<"{"; for(auto e:v)os< void dmpr(ostream&os,const T&t,const Args&... args){ os< ostream& operator<<(ostream&os,const array&a){ return os<(all(a)); } template void print_tuple(ostream&,const T&){ } template void print_tuple(ostream&os,const T&t){ if(i)os<<","; os<(t); print_tuple(os,t); } template ostream& operator<<(ostream&os,const tuple&t){ os<<"{"; print_tuple<0,tuple,Args...>(os,t); return os<<"}"; } template void print(t x,int suc=1){ cout<>i; return i; } vi readvi(int n,int off=0){ vi v(n); rep(i,n)v[i]=read()+off; return v; } pi readpi(int off=0){ int a,b;cin>>a>>b; return pi(a+off,b+off); } template void print(const vector&v,int suc=1){ rep(i,v.size()) print(v[i],i==int(v.size())-1?suc:2); } string readString(){ string s; cin>>s; return s; } template T sq(const T& t){ return t*t; } //#define CAPITAL void yes(bool ex=true){ #ifdef CAPITAL cout<<"YES"<<"\n"; #else cout<<"Yes"<<"\n"; #endif if(ex)exit(0); #ifdef LOCAL cout.flush(); #endif } void no(bool ex=true){ #ifdef CAPITAL cout<<"NO"<<"\n"; #else cout<<"No"<<"\n"; #endif if(ex)exit(0); #ifdef LOCAL cout.flush(); #endif } void possible(bool ex=true){ #ifdef CAPITAL cout<<"POSSIBLE"<<"\n"; #else cout<<"Possible"<<"\n"; #endif if(ex)exit(0); #ifdef LOCAL cout.flush(); #endif } void impossible(bool ex=true){ #ifdef CAPITAL cout<<"IMPOSSIBLE"<<"\n"; #else cout<<"Impossible"<<"\n"; #endif if(ex)exit(0); #ifdef LOCAL cout.flush(); #endif } constexpr ll ten(int n){ return n==0?1:ten(n-1)*10; } const ll infLL=LLONG_MAX/3; #ifdef int const int inf=infLL; #else const int inf=INT_MAX/2-100; #endif int topbit(signed t){ return t==0?-1:31-__builtin_clz(t); } int topbit(ll t){ return t==0?-1:63-__builtin_clzll(t); } int botbit(signed a){ return a==0?32:__builtin_ctz(a); } int botbit(ll a){ return a==0?64:__builtin_ctzll(a); } int popcount(signed t){ return __builtin_popcount(t); } int popcount(ll t){ return __builtin_popcountll(t); } bool ispow2(int i){ return i&&(i&-i)==i; } ll mask(int i){ return (ll(1)< void mkuni(vc&v){ sort(all(v)); v.erase(unique(all(v)),v.ed); } ll rand_int(ll l, ll r) { //[l, r] #ifdef LOCAL static mt19937_64 gen; #else static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count()); #endif return uniform_int_distribution(l, r)(gen); } template void myshuffle(vc&a){ rep(i,si(a))swap(a[i],a[rand_int(0,i)]); } template int lwb(const vc&v,const t&a){ return lower_bound(all(v),a)-v.bg; } vvc readGraph(int n,int m){ vvc g(n); rep(i,m){ int a,b; cin>>a>>b; //sc.read(a,b); a--;b--; g[a].pb(b); g[b].pb(a); } return g; } vvc readTree(int n){ return readGraph(n,n-1); } struct modinfo{uint mod,root;}; template struct modular{ static constexpr uint const &mod=ref.mod; static modular root(){return modular(ref.root);} uint v; //modular(initializer_listls):v(*ls.bg){} modular(ll vv=0){s(vv%mod+mod);} modular& s(uint vv){ v=vv>=1; } return res; } modular inv()const{return pow(mod-2);} /*modular inv()const{ int x,y; int g=extgcd(v,mod,x,y); assert(g==1); if(x<0)x+=mod; return modular(x); }*/ friend modular operator+(int x,const modular&y){ return modular(x)+y; } friend modular operator-(int x,const modular&y){ return modular(x)-y; } friend modular operator*(int x,const modular&y){ return modular(x)*y; } friend modular operator/(int x,const modular&y){ return modular(x)/y; } friend ostream& operator<<(ostream&os,const modular&m){ return os<>(istream&is,modular&m){ ll x;is>>x; m=modular(x); return is; } bool operator<(const modular&r)const{return v; const int vmax=(1<<21)+10; mint fact[vmax],finv[vmax],invs[vmax]; void initfact(){ fact[0]=1; rng(i,1,vmax){ fact[i]=fact[i-1]*i; } finv[vmax-1]=fact[vmax-1].inv(); for(int i=vmax-2;i>=0;i--){ finv[i]=finv[i+1]*(i+1); } for(int i=vmax-1;i>=1;i--){ invs[i]=finv[i]*fact[i-1]; } } mint choose(int n,int k){ return fact[n]*finv[n-k]*finv[k]; } mint binom(int a,int b){ return fact[a+b]*finv[a]*finv[b]; } mint catalan(int n){ return binom(n,n)-(n-1>=0?binom(n-1,n+1):0); } /* const int vmax=110; mint binbuf[vmax][vmax]; mint choose(int n,int k){ return binbuf[n-k][k]; } mint binom(int a,int b){ return binbuf[a][b]; } void initfact(){ binbuf[0][0]=1; rep(i,vmax)rep(j,vmax){ if(i)binbuf[i][j]+=binbuf[i-1][j]; if(j)binbuf[i][j]+=binbuf[i][j-1]; } } */ #define USE_GOOD_MOD //size of input must be a power of 2 //output of forward fmt is bit-reversed //output elements are in the range [0,mod*4) //input of inverse fmt should be bit-reversed template void inplace_fmt(const int n,mint*const f,bool inv){ static constexpr uint mod=mint::mod; static constexpr uint mod2=mod*2; static const int L=30; static mint g[L],ig[L],p2[L]; if(g[0].v==0){ rep(i,L){ mint w=-mint::root().pow(((mod-1)>>(i+2))*3); g[i]=w; ig[i]=w.inv(); p2[i]=mint(1<>=1){//input:[0,mod) rep(i,b){ uint x=f[i+b].v; f[i+b].v=f[i].v+mod-x; f[i].v+=x; } } if(b>>=1){//input:[0,mod*2) mint p=1; for(int i=0,k=0;i>=1){//input:[0,mod*3) mint p=1; for(int i=0,k=0;i>=1){//input:[0,mod*4) mint p=1; for(int i=0,k=0;i void inplace_fmt(vector&f,bool inv){ inplace_fmt(si(f),f.data(),inv); } template void half_fmt(const int n,mint*const f){ static constexpr uint mod=mint::mod; static constexpr uint mod2=mod*2; static const int L=30; static mint g[L],h[L]; if(g[0].v==0){ rep(i,L){ g[i]=-mint::root().pow(((mod-1)>>(i+2))*3); h[i]=mint::root().pow((mod-1)>>(i+2)); } } int b=n; int lv=0; if(b>>=1){//input:[0,mod) mint p=h[lv++]; for(int i=0,k=0;i>=1){//input:[0,mod*2) mint p=h[lv++]; for(int i=0,k=0;i>=1){//input:[0,mod*3) mint p=h[lv++]; for(int i=0,k=0;i>=1){//input:[0,mod*4) mint p=h[lv++]; for(int i=0,k=0;i void half_fmt(vector&f){ half_fmt(si(f),f.data()); } #ifdef USE_GOOD_MOD template vc multiply(vc x,const vc&y,bool same=false){ int n=si(x)+si(y)-1; int s=1; while(s z(s); rep(i,si(y))z[i]=y[i]; inplace_fmt(z,false); rep(i,s)x[i]*=z[i]; }else{ rep(i,s)x[i]*=x[i]; } inplace_fmt(x,true);x.resize(n); return x; } #else //59501818244292734739283969-1=5.95*10^25 までの値を正しく計算 //最終的な列の大きさが 2^24 までなら動く //最終的な列の大きさが 2^20 以下のときは,下の 3 つの素数を使ったほうが速い(は?) //VERIFY: yosupo //Yukicoder No980 (same=true) namespace arbitrary_convolution{ //constexpr modinfo base0{167772161,3};//2^25 * 5 + 1 //constexpr modinfo base1{469762049,3};//2^26 * 7 + 1 //constexpr modinfo base2{754974721,11};//2^24 * 45 + 1 extern constexpr modinfo base0{1045430273,3};//2^20 * 997 + 1 extern constexpr modinfo base1{1051721729,6};//2^20 * 1003 + 1 extern constexpr modinfo base2{1053818881,7};//2^20 * 1005 + 1 using mint0=modular; using mint1=modular; using mint2=modular; template vc sub(const vc&x,const vc&y,bool same=false){ int n=si(x)+si(y)-1; int s=1; while(s z(s);rep(i,si(x))z[i]=x[i].v; inplace_fmt(z,false); if(!same){ vc w(s);rep(i,si(y))w[i]=y[i].v; inplace_fmt(w,false); rep(i,s)z[i]*=w[i]; }else{ rep(i,s)z[i]*=z[i]; } inplace_fmt(z,true);z.resize(n); return z; } template vc multiply(const vc&x,const vc&y,bool same=false){ auto d0=sub(x,y,same); auto d1=sub(x,y,same); auto d2=sub(x,y,same); int n=si(d0); vc res(n); static const mint1 r01=mint1(mint0::mod).inv(); static const mint2 r02=mint2(mint0::mod).inv(); static const mint2 r12=mint2(mint1::mod).inv(); static const mint2 r02r12=r02*r12; static const mint w1=mint(mint0::mod); static const mint w2=w1*mint(mint1::mod); rep(i,n){ ull a=d0[i].v; ull b=(d1[i].v+mint1::mod-a)*r01.v%mint1::mod; ull c=((d2[i].v+mint2::mod-a)*r02r12.v+(mint2::mod-b)*r12.v)%mint2::mod; res[i].v=(a+b*w1.v+c*w2.v)%mint::mod; } return res; } } using arbitrary_convolution::multiply; #endif namespace integer_convolution{ extern constexpr modinfo base0{1045430273,3};//2^20 * 997 + 1 extern constexpr modinfo base1{1051721729,6};//2^20 * 1003 + 1 using mint0=modular; using mint1=modular; template vc sub(const vi&x,const vi&y,bool same=false){ int n=si(x)+si(y)-1; int s=1; while(s z(s);rep(i,si(x))z[i]=x[i]; inplace_fmt(z,false); if(!same){ vc w(s);rep(i,si(y))w[i]=y[i]; inplace_fmt(w,false); rep(i,s)z[i]*=w[i]; }else{ rep(i,s)z[i]*=z[i]; } inplace_fmt(z,true);z.resize(n); return z; } vi multiply(const vi&x,const vi&y,bool same=false){ auto d0=sub(x,y,same); auto d1=sub(x,y,same); const mint1 r=mint1(mint0::mod).inv(); int n=si(d0); vi res(n); rep(i,n){ res[i]=d0[i].v+(r*(d1[i]-d0[i].v)).v*(ull)mint0::mod; } return res; } } //最大で 1< vc large_convolution(const vc&a,const vc&b,int mx){ int n=si(a),m=si(b); vc c(n+m-1); int len=1<<(mx-1); for(int i=0;i(a.bg+i,a.bg+i+x),vc(b.bg+j,b.bg+j+y)); rep(k,si(d)) c[i+j+k]+=d[k]; } } return c; } //[0-m-1],[m,2*m-1]...[nm-m,nm-1] vc fmt_2d(vc f,int n,int m,bool inv){ rep(i,n)inplace_fmt(m,&f[i*m],inv); rep(j,m){ vc tmp(n); rep(i,n)tmp[i]=mint(f[i*m+j].v); inplace_fmt(tmp,inv); rep(i,n)f[i*m+j]=mint(tmp[i].v); } return f; } signed main(){ cin.tie(0); ios::sync_with_stdio(0); cout<>x>>y>>t>>a>>b>>c>>d; a--;b--;c--;d--; int n=1< f(n*2*m*2); auto idx=[&](int i,int j){ return i*m*2+j; }; f[idx(0,0)]+=1; f[idx(1,0)]+=1; f[idx(0,1)]+=1; f[idx(n*2-1,0)]+=1; f[idx(0,m*2-1)]+=1; auto g=fmt_2d(f,n*2,m*2,false); rep(i,n*2*m*2)g[i]=g[i].pow(t%(mint::mod-1)); auto h=fmt_2d(g,n*2,m*2,true); dmp(h); rep(i,2*n){ dmp(vc(h.begin()+i*2*m,h.begin()+(i+1)*2*m)); } mint ans=0; rep(_,2){ rep($,2){ dmp2(c,d); int dx=(c-a+2*n)%(2*n); int dy=(d-b+2*m)%(2*m); dmp2(dx,dy); ans+=h[idx(dx,dy)]*((_^$)?-1:1); d=2*(m-1)-d; } c=2*(n-1)-c; } cout<