#line 1 "library/Template/template.hpp" #include using namespace std; #define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++) #define ALL(v) (v).begin(),(v).end() #define UNIQUE(v) sort(ALL(v)),(v).erase(unique(ALL(v)),(v).end()) #define MIN(v) *min_element(ALL(v)) #define MAX(v) *max_element(ALL(v)) #define LB(v,x) lower_bound(ALL(v),(x))-(v).begin() #define UB(v,x) upper_bound(ALL(v),(x))-(v).begin() using ll=long long int; const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; templateinline bool chmax(T& a,T b){if(ainline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;} templateT ceil(T x,U y){assert(y!=0); if(y<0)x=-x,y=-y; return (x>0?(x+y-1)/y:x/y);} templateT floor(T x,U y){assert(y!=0); if(y<0)x=-x,y=-y; return (x>0?x/y:(x-y+1)/y);} templateint popcnt(T x){return __builtin_popcountll(x);} templateint topbit(T x){return (x==0?-1:63-__builtin_clzll(x));} templateint lowbit(T x){return (x==0?-1:__builtin_ctzll(x));} #line 2 "library/Utility/fastio.hpp" #include class FastIO{ static constexpr int L=1<<16; char rdbuf[L]; int rdLeft=0,rdRight=0; inline void reload(){ int len=rdRight-rdLeft; memmove(rdbuf,rdbuf+rdLeft,len); rdLeft=0,rdRight=len; rdRight+=fread(rdbuf+len,1,L-len,stdin); } inline bool skip(){ for(;;){ while(rdLeft!=rdRight and rdbuf[rdLeft]<=' ')rdLeft++; if(rdLeft==rdRight){ reload(); if(rdLeft==rdRight)return false; } else break; } return true; } template::value,int> =0>inline bool _read(T& x){ if(!skip())return false; if(rdLeft+20>=rdRight)reload(); bool neg=false; if(rdbuf[rdLeft]=='-'){ neg=true; rdLeft++; } x=0; while(rdbuf[rdLeft]>='0' and rdLeft=rdRight)reload(); bool neg=false; if(rdbuf[rdLeft]=='-'){ neg=true; rdLeft++; } x=0; while(rdbuf[rdLeft]>='0' and rdLeft=rdRight)reload(); x=0; while(rdbuf[rdLeft]>='0' and rdLeft::value,int> =0>inline bool _read(T& x){ if(!skip())return false; if(rdLeft+20>=rdRight)reload(); bool neg=false; if(rdbuf[rdLeft]=='-'){ neg=true; rdLeft++; } x=0; while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft='0' and rdbuf[rdLeft]<='9' and rdLeft=rdRight)reload(); x=rdbuf[rdLeft++]; return true; } inline bool _read(string& x){ if(!skip())return false; for(;;){ int pos=rdLeft; while(pos' ')pos++; x.append(rdbuf+rdLeft,pos-rdLeft); if(rdLeft==pos)break; rdLeft=pos; if(rdLeft==rdRight)reload(); else break; } return true; } templateinline bool _read(vector& v){ for(auto& x:v){ if(!_read(x))return false; } return true; } char wtbuf[L],tmp[50]; int wtRight=0; inline void flush(){ fwrite(wtbuf,1,wtRight,stdout); wtRight=0; } inline void _write(const char& x){ if(wtRight>L-32)flush(); wtbuf[wtRight++]=x; } inline void _write(const string& x){ for(auto& c:x)_write(c); } template::value,int> =0>inline void _write(T x){ if(wtRight>L-32)flush(); if(x==0){ _write('0'); return; } else if(x<0){ _write('-'); if (__builtin_expect(x == std::numeric_limits::min(), 0)) { switch (sizeof(x)) { case 2: _write("32768"); return; case 4: _write("2147483648"); return; case 8: _write("9223372036854775808"); return; } } x=-x; } int pos=0; while(x!=0){ tmp[pos++]=char((x%10)|48); x/=10; } rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i]; wtRight+=pos; } inline void _write(__int128_t x){ if(wtRight>L-40)flush(); if(x==0){ _write('0'); return; } else if(x<0){ _write('-'); x=-x; } int pos=0; while(x!=0){ tmp[pos++]=char((x%10)|48); x/=10; } rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i]; wtRight+=pos; } inline void _write(__uint128_t x){ if(wtRight>L-40)flush(); if(x==0){ _write('0'); return; } int pos=0; while(x!=0){ tmp[pos++]=char((x%10)|48); x/=10; } rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i]; wtRight+=pos; } templateinline void _write(const vector& v){ rep(i,0,v.size()){ if(i)_write(' '); _write(v[i]); } } public: FastIO(){} ~FastIO(){flush();} inline void read(){} template inline void read(Head& head,Tail&... tail){ assert(_read(head)); read(tail...); } templateinline void write(){if(ln)_write('\n');} template inline void write(const Head& head,const Tail&... tail){ if(space)_write(' '); _write(head); write(tail...); } }; /** * @brief Fast IO */ #line 3 "sol.cpp" #line 2 "library/Math/modint.hpp" templatestruct fp { int v; static constexpr int get_mod(){return mod;} int inv() const{ int tmp,a=v,b=mod,x=1,y=0; while(b)tmp=a/b,a-=tmp*b,swap(a,b),x-=tmp*y,swap(x,y); if(x<0){x+=mod;} return x; } fp(ll x=0){init(x%mod+mod);} fp& init(ll x){v=(x=0); fp res=1,b=*this; while(t){if(t&1)res*=b;b*=b;t>>=1;} return res;} fp& operator+=(const fp& x){return init(v+x.v);} fp& operator-=(const fp& x){return init(v+mod-x.v);} fp& operator*=(const fp& x){v=ll(v)*x.v%mod; return *this;} fp& operator/=(const fp& x){v=ll(v)*x.inv()%mod; return *this;} fp operator+(const fp& x)const{return fp(*this)+=x;} fp operator-(const fp& x)const{return fp(*this)-=x;} fp operator*(const fp& x)const{return fp(*this)*=x;} fp operator/(const fp& x)const{return fp(*this)/=x;} bool operator==(const fp& x)const{return v==x.v;} bool operator!=(const fp& x)const{return v!=x.v;} friend istream& operator>>(istream& is,fp& x){return is>>x.v;} friend ostream& operator<<(ostream& os,const fp& x){return os<; #line 2 "library/DataStructure/segtreebeats.hpp" struct Segtreebeats{ struct state{ ll maxx=-INF,smax=-INF,cmax=0,lmax=-INF; ll minn=INF,smin=INF,cmin=0,lmin=INF; ll sum=0,add=0; int len=1; state(){} state(ll val):maxx(val),cmax(1),minn(val),cmin(1),sum(val){} }; int n; vector val; Segtreebeats(int _n):Segtreebeats(vector(_n,0)){} Segtreebeats(const vector& a){ for(n=1;n<(int)a.size();n<<=1); val.assign(2*n,state()); rep(i,0,a.size())val[i+n]=state(a[i]); for(int i=n-1;i;i--)apply(i); } void apply(int k){ state &x=val[k],&lb=val[2*k],&rb=val[2*k+1]; if(lb.minnrb.minn)x.minn=rb.minn,x.cmin=rb.cmin,x.smin=min(rb.smin,lb.minn); else x.minn=lb.minn,x.cmin=lb.cmin+rb.cmin,x.smin=min(lb.smin,rb.smin); if(lb.maxx>rb.maxx)x.maxx=lb.maxx,x.cmax=lb.cmax,x.smax=max(lb.smax,rb.maxx); else if(lb.maxx=x.smin){eval(k*2); eval(k*2+1); apply(k);} else if(x.lmax>x.minn){ x.sum+=x.cmin*(x.lmax-x.minn); if(x.smax==x.minn)x.smax=x.lmax; if(x.maxx==x.minn)x.maxx=x.lmax; x.minn=x.lmax; } x.lmax=-INF; } if(x.lmin!=INF){ chmin(lb.lmax,x.lmin); chmin(lb.lmin,x.lmin); chmin(rb.lmax,x.lmin); chmin(rb.lmin,x.lmin); if(x.lmin<=x.smax){eval(k*2); eval(k*2+1); apply(k);} else if(x.lmin=r)return; if(b>=r&&a<=l){ val[k].add=c; eval(k); }else{ range_add(a,b,c,k*2,l,(l+r)/2); range_add(a,b,c,k*2+1,(l+r)/2,r); apply(k); } } void range_chmin(int a,int b,ll c,int k=1,int l=0,int r=-1){ if(r<0)r=n; eval(k); if(b<=l||a>=r)return; if(b>=r&&a<=l){ val[k].lmin=c; eval(k); }else{ range_chmin(a,b,c,k*2,l,(l+r)/2); range_chmin(a,b,c,k*2+1,(l+r)/2,r); apply(k); } } void range_chmax(int a,int b,ll c,int k=1,int l=0,int r=-1){ if(r<0)r=n; eval(k); if(b<=l||a>=r)return; if(b>=r&&a<=l){ val[k].lmax=c; eval(k); }else{ range_chmax(a,b,c,k*2,l,(l+r)/2); range_chmax(a,b,c,k*2+1,(l+r)/2,r); apply(k); } } ll query_max(int a,int b,int k=1,int l=0,int r=-1){ if(r<0)r=n; eval(k); if(b<=l||a>=r)return -INF; if(b>=r&&a<=l)return val[k].maxx; else{ ll res=max(query_max(a,b,k*2,l,(l+r)/2),query_max(a,b,k*2+1,(l+r)/2,r)); return res; } } ll query_min(int a,int b,int k=1,int l=0,int r=-1){ if(r<0)r=n; eval(k); if(b<=l||a>=r)return INF; if(b>=r&&a<=l)return val[k].minn; else{ ll res=min(query_min(a,b,k*2,l,(l+r)/2),query_min(a,b,k*2+1,(l+r)/2,r)); return res; } } ll query_sum(int a,int b,int k=1,int l=0,int r=-1){ if(r<0)r=n; eval(k); if(b<=l||a>=r)return 0; if(b>=r&&a<=l)return val[k].sum; else{ ll res=query_sum(a,b,k*2,l,(l+r)/2)+query_sum(a,b,k*2+1,(l+r)/2,r); return res; } } }; /** * @brief Segment Tree Beats */ #line 7 "sol.cpp" FastIO io; int main(){ int n,q; io.read(n,q); vector a(n); io.read(a); vector Z(30,Segtreebeats(n)); vector O(30,Segtreebeats(n)); rep(k,0,30)O[k].range_chmax(0,n,1); // vector _z(n),_o(n,(1<<30)-1); rep(i,0,q){ char c; int L,R,x; io.read(c,L,R,x); L--; if(c=='o'){ rep(k,0,30)if(x>>k&1){ Z[k].range_chmax(L,R,1); O[k].range_chmax(L,R,1); } // rep(i,L,R)_z[i]|=x,_o[i]|=x; } else{ rep(k,0,30)if(x>>k&1){ Z[k].range_add(L,R,-1); O[k].range_add(L,R,-1); } // rep(i,L,R)_z[i]^=x,_o[i]^=x; } } vector zero(n),one(n); rep(i,0,n){ rep(k,0,30){ if(Z[k].query_sum(i,i+1)&1)zero[i]|=(1<(32)); rep(i,0,n){ Fp dp[32][32][2]; dp[30][0][0]=1; for(int keta=29;keta>=0;keta--){ rep(cnt,0,31){ int ai=a[i]>>keta&1; rep(flag,0,2){ rep(nxt,0,2){ if(flag==0 and ainxt)nf=1; int add=0; if(nxt==0)add=zero[i]>>keta&1; else add=one[i]>>keta&1; dp[keta][cnt+add][nf]+=dp[keta+1][cnt][flag]; } } } } rep(cnt,0,32)rep(flag,0,2)calc[i][cnt]+=dp[0][cnt][flag]; } Fp ret,pre; rep(k,0,31){ Fp sub=1; rep(i,0,n){ Fp sum; rep(cnt,0,k+1)sum+=calc[i][cnt]; sub*=sum; } ret+=(sub-pre)*k; pre=sub; } io.write(ret.v); return 0; }