#pragma GCC target("avx2") #pragma GCC optimize("O3","unroll-loops") #include #include #define bgn(a) begin(a) #define rbg(a) rbegin(a) #define al(a) bgn(a),end(a) #define fin(...) rr vo(pp(__VA_ARGS__)) #define ep(...) emplace(__VA_ARGS__) #define eb(...) emplace_back(__VA_ARGS__) #define ef(...) else if(__VA_ARGS__) #define el else #define wh(...) while(__VA_ARGS__) #define lb(...) lower_bound(__VA_ARGS__) #define ub(...) upper_bound(__VA_ARGS__) #define srt(...) sort(al(__VA_ARGS__)) #define rv(...) reverse(al(__VA_ARGS__)) #define rsr(a) srt(a),rv(a) #define uq(a) srt(a),a.erase(unique(al(a)),end(a)) #define ov4(a,b,c,d,e,...) e #define ov5(a,b,c,d,e,f,...) f #define fo1(b) for(ll ii=0;ii<(ll)(b);++ii) #define fo2(i,b) for(ll i=0;i<(ll)(b);++i) #define fo3(i,a,b) for(ll i=(ll)(a);i<(ll)(b);++i) #define fo4(i,a,b,c) for(ll i=(ll)(a);i<(ll)(b);i+=(ll)(c)) #define foo(...) ov4(__VA_ARGS__,fo4,fo3,fo2,fo1)(__VA_ARGS__) #define of2(i,a) for(ll i=(ll)(a)-1;i>=0;--i) #define of3(i,a,b) for(ll i=(ll)(a)-1;i>=(ll)(b);--i) #define of4(i,a,b,c) for(ll i=(ll)(a)-1;i>=(ll)(b);i-=(ll)(c)) #define oof(...) ov4(__VA_ARGS__,of4,of3,of2)(__VA_ARGS__) #define fe2(a,v) for(au&&a:v) #define fe3(a,b,v) for(au&&[a,b]:v) #define fe4(a,b,c,v) for(au&&[a,b,c]:v) #define fe5(a,b,c,d,v) for(au&&[a,b,c,d]:v) #define fee(...) ov5(__VA_ARGS__,fe5,fe4,fe3,fe2)(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;li(__VA_ARGS__) #define DD(...) dd __VA_ARGS__;li(__VA_ARGS__) #define CH(...) char __VA_ARGS__;li(__VA_ARGS__) #define ST(...) str __VA_ARGS__;li(__VA_ARGS__) #define UL2(n,a) u1 a(n);li(a) #define UL3(n,a,b) u1 a(n),b(n);li(a,b) #define UL4(n,a,b,c) u1 a(n),b(n),c(n);li(a,b,c) #define UL5(n,a,b,c,d) u1 a(n),b(n),c(n),d(n);li(a,b,c,d) #define UL(...) ov5(__VA_ARGS__,UL5,UL4,UL3,UL2)(__VA_ARGS__) #define UV3(n,a,b) u1 a(n),b(n);vi(a,b) #define UV4(n,a,b,c) u1 a(n),b(n),c(n);vi(a,b,c) #define UV5(n,a,b,c,d) u1 a(n),b(n),c(n),d(n);vi(a,b,c,d) #define UV(...) ov5(__VA_ARGS__,UV5,UV4,UV3)(__VA_ARGS__) #define U2(h,w,a) u2 a(h,w);li(a) #define I template #define J typename #define O operator #define rr return #define uu using #define au auto #define cs const namespace atcoder{}namespace my{void main();void solve();}int main(){my::main();} namespace my{uu namespace std;uu namespace atcoder; uu is=istream;uu os=ostream;uu vo=void;uu bo=bool;uu ll=long long;uu dd=long double;uu i128=__int128_t; uu ml=modint998244353; Iuu v1=vector; Istruct v2:v1>{uu v1>::v1;v2(ll a,ll b,T x=T{}){this->resize(a,v1(b,x));}}; Istruct v3:v1>{uu v1>::v1;v3(ll a,ll b,ll c,T x=T{}){this->resize(a,v2(b,c,x));}}; Istruct v4:v1>{uu v1>::v1;v4(ll a,ll b,ll c,ll d,T x=T{}){this->resize(a,v3(b,c,d,x));}}; Istruct v5:v1>{uu v1>::v1;v5(ll a,ll b,ll c,ll d,ll e,T x=T{}){this->resize(a,v4(b,c,d,e,x));}}; uu u1=v1;uu u2=v2;uu u3=v3;uu u4=v4;uu m1=v1;uu m2=v2;uu m3=v3;uu m4=v4;uu m5=v5; uu str=string;uu strs=v1;str sp=" ",nc="",nl="\n";str Yes(bo y=1){rr y?"Yes":"No";}str No(){rr Yes(0);} Istruct cp{ A a;B b;cp():a(A{}),b(B{}){}cp(A a,B b):a(a),b(b){}cp(pairp):a(p.first),b(p.second){} cp&O+=(cs cp&c){a+=c.a,b+=c.b;rr*this;}cp O+(cs cp&c)cs{rr cp{*this}+=c;} cp&O-=(cs cp&c){a-=c.a,b-=c.b;rr*this;}cp O-(cs cp&c)cs{rr cp{*this}-=c;}cp O-()cs{rr cp(-a,-b);} Icp&O+=(cs T&x){a+=x,b+=x;rr*this;}Icp O+(cs T&x)cs{rr cp{*this}+=x;} Icp&O-=(cs T&x){a-=x;b-=x;rr*this;}Icp O-(cs T&x)cs{rr cp{*this}-=x;} Icp&O*=(cs T&x){a*=x;b*=x;rr*this;}Icp O*(cs T&x)cs{rr cp{*this}*=x;} au abs()cs{rr std::abs(a)+std::abs(b);}au abs(cs cp&c)cs{rr(*this-c).abs();} bo O==(cs cp&c)cs{rr a==c.a&&b==c.b;}bo O!=(cs cp&c)cs{rr!(*this==c);} bo O<(cs cp&c)cs{rr a!=c.a?a(cs cp&c)cs{rr a!=c.a?a>c.a:b>c.b;} friend is&O>>(is&i,cp&c){rr i>>c.a>>c.b;}friend os&O<<(os&o,cs cp&c){rr o<;uu cls=v1; Istruct tr{ A a;B b;C c;tr():a(A{}),b(B{}),c(C{}){}tr(A a,B b,C c):a(a),b(b),c(c){} bo O==(cs tr&t)cs{rr a==t.a&&b==t.b&&c==t.c;} bo O<(cs tr&t)cs{rr a!=t.a?a(cs tr&t)cs{rr a!=t.a?a>t.a:b!=t.b?b>t.b:c>t.c;} friend is&O>>(is&i,tr&t){rr i>>t.a>>t.b>>t.c;}friend os&O<<(os&o,cs tr&t){rr o<;uu tls=v1; Istruct qu{ A a;B b;C c;D d;qu():a(A{}),b(B{}),c(C{}),d(D{}){}qu(A a,B b,C c,D d):a(a),b(b),c(c),d(d){} bo O==(cs qu&q)cs{rr a==q.a&&b==q.b&&c==q.c&&d==q.d;} bo O<(cs qu&q)cs{rr a!=q.a?a(cs qu&q)cs{rr a!=q.a?a>q.a:b!=q.b?b>q.b:c!=q.c?c>q.c:d>q.d;} friend os&O<<(os&o,cs qu&q){rr o<;uu qls=v1; Istruct set:std::set{set(){}set(cs v1&a){fee(e,a)this->ep(e);}}; Istruct uset:unordered_set{uset(){}uset(cs v1&a){fee(e,a)this->ep(e);}}; Istruct mset:multiset{mset(){}mset(cs v1&a){fee(e,a)this->ep(e);}bo erase(cs T&x){bo c=this->count(x);if(c)multiset::erase(this->find(x));rr c;}}; Iuu fn=function;uu mp=map;uu ump=unordered_map;uu sl=set;uu usl=uset;uu msl=mset; Iuu qmax=priority_queue;Iuu qmin=priority_queue,greater>;uu dl=deque; ll oo=3e18;dd ee=1e-12,pi=acosl(-1);u1 dx{-1,0,1,0,-1,1,1,-1},dy{0,-1,0,1,-1,-1,1,1}; bo odd(ll x){rr x&1;}bo eve(ll x){rr !odd(x);}ll pm1(ll x){rr 1-2*(x&1);}ll pw2(ll n){rr 1LL<T sq(cs T&a){rr a*a;} ll cbr(ll x){if(x<=1)rr x;ll r=cbrtl(x)-1;wh(r+1<=x/(r+1)/(r+1))++r;rr r;}IT cb(cs T&a){rr a*a*a;} ll l2(i128 x){if(x<0)rr 0;x|=1;ll r=0;wh(x)x>>=1,++r;rr r;}ll l10(i128 x){if(x<0)rr 0;x|=1;ll r=0;wh(x)x/=10,++r;rr r;} ll msb(ll x){if(x==0)rr-1;rr l2(x)-1;}ll lsb(ll x){if(x==0)rr-1;rr __builtin_ctzll(x);} u1 io(ll n,ll x=0){u1 a(n);iota(al(a),x);rr a;} Iau sum(T a,U d,V n){rr n*(a*2+(n-1)*d)/2;} Ill len(cs T&a){rr a.size();}Ibo mu(cs T&a){rr !len(a);} Ibo at(T S,ll i){rr S>>i&1;}IT at(cs v1&v,ll i){ll n=len(v);rr v[(i%n+n)%n];} Ill sgn(cs T&a){rr(a>ee)-(a<-ee);}Ill sgn(cs T&a,cs U&b){rr sgn(a-b);} IT cei(T x,U y){assert(y);rr(y<0?cei(-x,-y):(x>0?(x+y-1)/y:x/y));} IT flo(T x,U y){assert(y);rr(y<0?flo(-x,-y):(x>0?x/y:x/y-(x%y!=0)));} IT rect(cs v1&s,ll l,ll r){assert(0<=l&&l<=r&&r<=len(s));T t{};if(r)t+=s[r-1];if(l)t-=s[l-1];rr t;} ll rp(ll a,ll x=oo,ll y=-1){rr a==x?y:a;}u1 rp(u1 a,ll x=oo,ll y=-1){foo(i,len(a))a[i]=rp(a[i],x,y);rr a;} Iau slice(cs v1&a,ll l,ll r){rr v1(bgn(a)+l,bgn(a)+r);} Ivo af(v1&v,U e=U{}){v.ep(bgn(v),e);}Ivo df(v1&v){v.erase(bgn(v));} Idecltype(au)bg(T&a){rr*bgn(a);}Idecltype(au)rb(T&a){rr*rbg(a);} IT pop(v1&v){T r=rb(v);v.pop_back();rr r;} IT pop(qmax&q){T r=q.top();q.pop();rr r;}IT pop(qmin&q){T r=q.top();q.pop();rr r;} IT pof(deque&q){T r=bg(q);q.pop_front();rr r;}IT pob(deque&q){T r=rb(q);q.pop_back();rr r;} Iau&O^=(v1&v,cs v1u){copy(al(u),back_inserter(v));rr v;}Iau O^(v1v,cs v1&u){rr v^=u;} Iau&O+=(v1&v,cs v1&u){foo(i,len(v))v[i]+=u[i];rr v;}Iau O+(v1v,cs v1&u){rr v+=u;} Iau&O-=(v1&v,cs v1&u){foo(i,len(v))v[i]-=u[i];rr v;}Iau O-(v1v,cs v1&u){rr v-=u;} Iau&O++(v1&v){fee(e,v)++e;rr v;}Iau O++(v1&v,int){au r=v;++v;rr r;} Iau&O--(v1&v){fee(e,v)--e;rr v;}Iau O--(v1&v,int){au r=v;--v;rr r;}Iau O-(v1v){fee(e,v)e*=-1;rr v;} Iau&O+=(v1&v,cs U a){fee(e,v)e+=a;rr v;}Iau O+(v1v,cs U&a){rr v+=a;} Iau&O-=(v1&v,cs U a){fee(e,v)e-=a;rr v;}Iau O-(v1v,cs U&a){rr v-=a;} Iau&O*=(v1&v,cs U a){fee(e,v)e*=a;rr v;}Iau O*(v1v,cs U&a){rr v*=a;} Iau&O/=(v1&v,cs U a){fee(e,v)e/=a;rr v;}Iau O/(v1v,cs U&a){rr v/=a;} Ibo amax(T&a,cs U&b){rr aau max(T...a){rr max(initializer_list>{a...});} Ibo amin(T&a,cs U&b){rr a>b?a=b,1:0;}Iau min(T...a){rr min(initializer_list>{a...});} IT max(cs v1&a){rr*max_element(al(a));}Iau max(cs v2&a){rr max(*max_element(al(a)));} IT min(cs v1&a){rr*min_element(al(a));}Iau min(cs v2&a){rr min(*min_element(al(a)));} IT sum(cs v1&a){rr accumulate(al(a),T{});}IT sum(cs v2&a){T r{};fee(e,a)r+=sum(e);rr r;} Ill lbs(cs v1&a,cs U&b){rr lb(al(a),b)-bgn(a);}Ill ubs(cs v1&a,cs U&b){rr ub(al(a),b)-bgn(a);} struct fio{fio(){cin.tie(0);ios::sync_with_stdio(0);cout<>(is&i,ml&x){ll t;i>>t;x=t;rr i;}os&O<<(os&o,cs ml&x){rr o<os&O<<(os&o,cs pair&p){rr o<os&O<<(os&o,qmaxq){wh(len(q))o<os&O<<(os&o,cs map&m){fee(p,m)o<os&O<<(os&o,qminq){wh(len(q))o<os&O<<(os&o,cs unordered_map&m){fee(p,m)o<os&O<<(os&o,cs v1&v){fee(e,v)o<is&O>>(is&i,v1&v){fee(e,v)i>>e;rr i;} Ios&O<<(os&o,cs v2&v){fee(e,v)o<ll pp(cs T&a,cs A&...b){cout<ll li(T&...a){(cin>>...>>a);rr 0;} Ivo vi(ll i,T&...a){(cin>>...>>a[i]);}Ivo vi(v1&a,A&...b){foo(i,len(a))vi(i,a,b...);} str ins(){str s;li(s);rr s;}strs ins2(ll n){strs s(n);li(s);rr s;} struct edg{ll t,w;edg(){}edg(ll t,ll w=1):t(t),w(w){}};uu graph=v2; u2 tou(cs graph&g){ll n=len(g);u2 a(n);foo(u,n)fee(v,w,g[u])a[u].eb(v);rr a;} graph tog(cs u2&a){ll n=len(a);graph g(n);foo(u,n)fee(v,a[u])g[u].eb(v);rr g;} au mgi(u2&g,ll m){UV(m,a,b);--a,--b;foo(i,m)g[a[i]].eb(b[i]),g[b[i]].eb(a[i]);rr tuple(a,b);} au ygi(u2&g,ll m){UV(m,a,b);--a,--b;foo(i,m)g[a[i]].eb(b[i]);rr tuple(a,b);} au mgi(graph&g,ll m){UV(m,a,b,c);--a,--b;foo(i,m)g[a[i]].eb(b[i],c[i]),g[b[i]].eb(a[i],c[i]);rr tuple(a,b,c);} au ygi(graph&g,ll m){UV(m,a,b,c);--a,--b;foo(i,m)g[a[i]].eb(b[i],c[i]);rr tuple(a,b,c);} au ti(u2&g){rr mgi(g,len(g)-1);}au ti(graph&g){rr mgi(g,len(g)-1);} au deco(cs u1&a,cs char&b='a'){str r{};fee(e,a)r+=e+b;rr r;} au deco(cs u2&a,cs char&b='a'){ll n=len(a);strs r(n);foo(i,n)r[i]=deco(a[i],b);rr r;} au deco(cs u1&a,cs str&b){ll n=len(a);str r(n,'$');foo(i,n)foo(j,len(b))if(a[i]==j){r[i]=b[j];break;}rr r;} au deco(cs u2&a,cs str&b){ll n=len(a);strs r(n);foo(i,n)r[i]=deco(a[i],b);rr r;} u1 enco(cs str&s,cs char&b='a'){u1 r;fee(c,s)r.eb(c-b);rr r;} u2 enco(cs strs&s,cs char&b='a'){u2 r;fee(e,s)r.eb(enco(e,b));rr r;} u1 enco(cs str&s,cs str&b){ll n=len(s);u1 r(n,-1);foo(i,n)foo(j,len(b))if(s[i]==b[j]){r[i]=j;break;}rr r;} u2 enco(cs strs&s,cs str&b){u2 r;fee(e,s)r.eb(enco(e,b));rr r;} Istruct rec:F{rec(F&&f):F(std::forward(f)){}Idecltype(au)O()(T&&...a)cs{rr F::O()(*this,std::forward(a)...);}}; Iau tzp(A&...a){v1v;fee(e,{a...})v^=e;uq(v);rr v;} vo pz(cs u1&v,u1&h){fee(e,h)e=lbs(v,e);}Ivo pz(cs u1&v,u1&h,T&...t){pz(v,h);pz(v,t...);} Iu1 zp(T&...a){u1 v=tzp(a...);pz(v,a...);rr v;}u1 zp(u2&a){u1 v;fee(e,a)v^=e;uq(v);fee(e,a)fee(x,e)x=lbs(v,x);rr v;} Ivo sv(cs u1&o,v1&a){au c=a;foo(i,len(a))a[i]=c[o[i]];}Ivo sv(cs u1&o,v1&a,A&...b){sv(o,a);sv(o,b...);} Iu1 vs(cs fn&f,v1&a){u1 o=io(len(a));sort(al(o),f);sv(o,a);rr o;} Iu1 vs(cs fn&f,v1&a,A&...b){u1 o=io(len(a));sort(al(o),f);sv(o,a);sv(o,b...);rr o;} ll bsl(cs fn&j,ll o,ll n){wh(abs(o-n)>1)(j((o+n)/2)?o:n)=(o+n)/2;rr o;} dd bsd(cs fn&j,dd o,dd n){wh(abs(o-n)>ee)(j((o+n)/2)?o:n)=(o+n)/2;rr o;} Iau zt(v1a){foo(i,1,len(a))a[i]+=a[i-1];rr a;}Iau zt(v2a){fee(v,a)v=zt(v);foo(i,1,len(a))a[i]+=a[i-1];rr a;} Iau mb(v1a){oof(i,len(a),1)a[i]-=a[i-1];rr a;}Iau mb(v2a){fee(v,a)v=mb(v);oof(i,len(a),1)a[i]-=a[i-1];rr a;} au rle(cs u1&a){cls r;fee(e,a)len(r)&&e==rb(r).a?++rb(r).b,0:(r.eb(e,1),0);rr r;} au rce(cs u1&a){cls r;ump m;fee(e,a)++m[e];fee(k,v,m)r.eb(k,v);rr uq(r),r;} u1 divs(ll n){u1 r;foo(i,1,n/i+1)if(n%i==0)r.eb(i),r.eb(n/i);rr uq(r),r;} mp fact(ll n){ump m;foo(i,2,n/i+1)wh(n%i==0)++m[i],n/=i;if(n>1)++m[n];rr mp(al(m));} i128 inv(i128 a,i128 m){a=(a%m+m)%m;i128 b=m,u=1,v=0;wh(b)u-=a/b*v,swap(u,v),a-=a/b*b,swap(a,b);rr(u%m+m)%m;} i128 pow(i128 x,i128 n){assert(n>=0);i128 r=1;wh(n){if(n&1)r*=x;x*=x,n>>=1;}rr r;} i128 pow(i128 x,i128 n,i128 m){if(n<0)n=-n,x=inv(x,m);i128 r=1;wh(n){if(n&1)r*=x,r%=m;x*=x,x%=m,n>>=1;}rr r;} vo main(){ll T=1;foo(T)solve();} vo solve(){ LL(N,X,Q); dsu uf(N); u1 d(N); ll A=30; u3 cnt(N,A,2); u2 g(N); foo(i,N){ g[i].eb(i); foo(b,A)cnt[i][b][0]=1; } m1 pw2(A); foo(i,A)pw2[i]=ml(2).pow(i); foo(i,Q){ LL(f); if(f==1){ LL(u,w); ll v=X; if(uf.same(u,v))continue; ll ul=uf.leader(u),vl=uf.leader(v); ll nl=uf.merge(u,v),ol=(nl!=ul?ul:vl); ll du=d[u],dv=d[v]; fee(x,g[ol]){ g[nl].eb(x); d[x]^=du^w^dv; foo(b,A)cnt[nl][b][at(d[x],b)]++; } g[ol].clear(); }ef(f==2){ LL(u,v); if(uf.same(u,v)){ pp(d[u]^d[v]); X+=d[u]^d[v],X%=N; }el{ pp(-1); } }ef(f==3){ LL(u); ll l=uf.leader(u); ml res=0; foo(b,A)res+=pw2[b]*cnt[l][b][0]*cnt[l][b][1]; pp(res); }ef(f==4){ LL(x); X+=x,X%=N; } } }}