You are given an undirected graph consisting of n vertices and  edges. Instead of giving you the edges that exist in the graph, we give you m unordered pairs (x, y) such that there is no edge between x and y, and if some pair of vertices is not listed in the input, then there is an edge between these vertices.

You have to find the number of connected components in the graph and the size of each component. A connected component is a set of vertices X such that for every two vertices from this set there exists at least one path in the graph connecting these vertices, but adding any other vertex to X violates this rule.

The first line contains two integers n and m (1 ≤ n ≤ 200000, ).

Then m lines follow, each containing a pair of integers x and y (1 ≤ x, y ≤ n, x ≠ y) denoting that there is no edge between x and y. Each pair is listed at most once; (x, y) and (y, x) are considered the same (so they are never listed in the same test). If some pair of vertices is not listed in the input, then there existsan edge between those vertices.

Firstly print k — the number of connected components in this graph.

Then print k integers — the sizes of components. You should output these integers in non-descending order.

 /*

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 */

 #include<iostream>

 #include<cstdio>

 #include<cstring>

 #include<ctime>

 #include<cstdlib>

 #include<algorithm>

 #include<cmath>

 #include<string>

 #include<map>

 #include<set>

 using namespace std;

 int read(){

     int xx=,ff=;char ch=getchar();

     while(ch>''||ch<''){if(ch=='-')ff=-;ch=getchar();}

     while(ch>=''&&ch<=''){xx=(xx<<)+(xx<<)+ch-'';ch=getchar();}

     return xx*ff;

 }

 const int maxn=;

 int N,M,t1,t2,temp[maxn],ans;

 set<int>s;

 map<int,bool>e[maxn];

 void dfs(int x){

     int prev=;

     while(){

         int t=*s.lower_bound(prev);

         if(t==(<<))

             break;

         prev=t+;

         if(!e[x][t]){

             temp[ans]++;

             s.erase(t);

             dfs(t);

         }

     }

 }

 int main(){

     //freopen("in","r",stdin);

     N=read(),M=read();

     for(int i=;i<=N;i++)

         s.insert(i);

     s.insert(<<);

     for(int i=;i<=M;i++){

         t1=read(),t2=read();

         e[t1][t2]=e[t2][t1]=;

     }

     int prev=;

     while(){

         int t=*s.lower_bound(prev);

         if(t==(<<))

             break;

         prev=t+;

         s.erase(t);

         temp[++ans]=;

         dfs(t);

     }

     sort(temp+,temp++ans);

     printf("%d\n",ans);

     for(int i=;i<=ans;i++)

         printf("%d ",temp[i]);

     puts("");

     return ;

 }

 /*

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 */

 #include<iostream>

 #include<cstdio>

 #include<cstring>

 #include<ctime>

 #include<cstdlib>

 #include<algorithm>

 #include<cmath>

 #include<string>

 using namespace std;

 inline int read(){

     int xx=,ff=;char ch=getchar();

     while(ch>''||ch<''){if(ch=='-')ff=-;ch=getchar();}

     while(ch>=''&&ch<=''){xx=(xx<<)+(xx<<)+ch-'';ch=getchar();}

     return xx*ff;

 }

 inline int mymin(int xx,int yy)

 {if(xx<yy)return xx;return yy;}

 const int maxn=,limit=;

 int N,M,D[limit+],tot=,sum[maxn],a[maxn];

 struct Segment_Tree{

     long long sum;

 }T[maxn*];

 int x,y,opt;

 void build(int L,int R,int root){

     if(L==R){

         T[root].sum=a[L];

         return;

     }

     int mid=(L+R)>>;

     build(L,mid,root*);

     build(mid+,R,root*+);

     T[root].sum=T[root*].sum+T[root*+].sum;

 }

 void upd(int L,int R,int root){

     if(T[root].sum==(R-L+)*)

         return;

     if(x>R||y<L)

         return;

     if(L==R){

         T[root].sum=D[T[root].sum];

         return;

     }

     int mid=(L+R)>>;

     upd(L,mid,root*);

     upd(mid+,R,root*+);

     T[root].sum=T[root*].sum+T[root*+].sum;

 }

 long long query(int L,int R,int root){

     if(x>R||y<L)

         return ;

     if(x<=L&&y>=R)

         return T[root].sum;

     int mid=(L+R)>>;

     return query(L,mid,root*)+query(mid+,R,root*+);

 }

 int main(){

     //freopen("in","r",stdin);

     for(int i=;i<=limit;i++)

         for(int j=i;j<=limit;j+=i)

             D[j]++;

     N=read(),M=read();

     for(int i=;i<=N;i++){

         a[i]=read();

         sum[i]=sum[i-];

         if(a[i]==)

             a[i]=,sum[i]++;

     }

     build(,N,);

     while(M--){

         opt=read();

         if(opt==){

             x=read(),y=read();

             upd(,N,);

         }

         else{

             x=read(),y=read();

             printf("%I64d\n",query(,N,)-(sum[y]-sum[x-]));

         }

     }

     return ;

 }

5 seconds

256 megabytes

standard input

standard output

 /*

 Welcome Hacking

 Wish You High Rating

 */

 #include<iostream>

 #include<cstdio>

 #include<cstring>

 #include<ctime>

 #include<cstdlib>

 #include<algorithm>

 #include<cmath>

 #include<string>

 #include<vector>

 using namespace std;

 int read(){

     int xx=,ff=;char ch=getchar();

     while(ch>''||ch<''){if(ch=='-')ff=-;ch=getchar();}

     while(ch>=''&&ch<=''){xx=(xx<<)+(xx<<)+ch-'';ch=getchar();}

     return xx*ff;

 }

 const int limit=;

 vector<int>V[limit+];

 void get_fac(){

     for(int i=;i<=limit;i++)

         if(!V[i].size())

             for(int j=i;j<=limit;j+=i)

                 V[j].push_back(i);

 }

 int x,p,k,delta;

 int L,R,mid;

 int calc(int num,int rb){

     int siz=V[num].size();

     int re=;

     for(int i=;i<(<<siz);i++){

         int s=,tim=;

         for(int j=;j<siz;j++)

             if((i>>j)&)

                 s*=V[num][j],tim++;

         if(tim&)

             re+=rb/s;

         else

             re-=rb/s;

     }

     return rb-re;

 }

 int main(){

     //freopen("in","r",stdin);

     get_fac();

     for(int T=read();T;T--){

         x=read(),p=read(),k=read();

         delta=calc(p,x);

         L=x,R=int(1e8);

         while(L+<R){

             mid=(L+R)/;

             if(calc(p,mid)-delta>=k)

                 R=mid;

             else

                 L=mid;

         }

         printf("%d\n",R);

     }

     return ;

 }