#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/dualsegtree.hpp" templateclass DualSegmentTree{ int sz,height; vector data; void down(int k){ data[k*2]=f(data[k*2],data[k]); data[k*2+1]=f(data[k*2+1],data[k]); data[k]=m1(); } public: DualSegmentTree(){} DualSegmentTree(int n){ sz=1,height=0; while(sz& v){ for(int i=0;i<(int)v.size();i++)data[i+sz]=v[i]; } void update(int a,int b,M x){ if(a>=b)return; a+=sz,b+=sz; for(int i=height;i;i--){ if(((a>>i)<>i); if(((b>>i)<>i); } for(;a>=1,b>>=1){ if(a&1)data[a]=f(data[a],x),a++; if(b&1)--b,data[b]=f(data[b],x); } } M query(int k){ k+=sz; for(int i=height;i;i--){ if(((k>>i)<>i); } M ret=data[k]; while(k>>=1)ret=f(ret,data[k]); return ret; } }; /** * @brief Dual Segment Tree */ #line 8 "sol.cpp" using P=pair; int ALL=(1<<30)-1; P f(P a,P b){ return P{(~a.first&b.first)|(a.first&b.second),(~a.second&b.first)|(a.second&b.second)}; } P m1(){ return P{0,ALL}; } FastIO io; int main(){ int n,q; io.read(n,q); vector a(n); io.read(a); DualSegmentTree seg(n); // 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'){ seg.update(L,R,P{x,ALL}); // rep(i,L,R)_z[i]|=x,_o[i]|=x; } else{ seg.update(L,R,P{x,ALL^x}); // rep(i,L,R)_z[i]^=x,_o[i]^=x; } } vector zero(n),one(n); rep(i,0,n){ auto [x1,x2]=seg.query(i); zero[i]=x1,one[i]=x2; } // io.write(zero); // io.write(_z); // return 0; vector calc(n,vector(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; }