给定一个有 nnn 个顶点的有向图，每个顶点有且仅有一条出边。每次询问给出两个顶点 aia_ia​i​​ 和 bib_ib​i​​，求满足以下条件的 xix_ix​i​​ 和 yiy_iy​i​​：

• 从顶点 aia_ia​i​​ 沿出边走 xix_ix​i​​ 步与从顶点 bib_ib​i​​ 沿出边走 yiy_iy​i​​ 步到达的顶点相同。
• max(xi,yi)\max(x_i, y_i)max(x​i​​,y​i​​) 最小。
• 满足以上条件的情况下 min(xi,yi)\min(x_i, y_i)min(x​i​​,y​i​​) 最小。
• 如果以上条件没有给出一个唯一的解，则还需要满足 xi≥yix_i \ge y_ix​i​​≥y​i​​.

如果不存在这样的 xix_ix​i​​ 和 yiy_iy​i​​，则 xi=yi=−1x_i = y_i = -1x​i​​=y​i​​=−1.

第一行两个正整数 nnn 和 kkk（1≤n≤500 000,1≤k≤500 0001 \le n \le 500\ 000,1 \le k \le 500\ 0001≤n≤500 000,1≤k≤500 000），表示顶点数和询问个数。

接下来一行 nnn 个正整数，第 iii 个数表示 iii 号顶点出边指向的顶点。

接下来 kkk 行表示询问，每行两个整数 aia_ia​i​​ 和 bib_ib​i​​.

对每组询问输出两个整数 xix_ix​i​​ 和 yiy_iy​i​​.

样例输入

12 5
4 3 5 5 1 1 12 12 9 9 7 1
7 2
8 11
1 2
9 10
10 5

样例输出

2 3
1 2
2 2
0 1
-1 -1

对于 40%40\%40% 的数据，n≤2000,k≤2000n \le 2000,k \le 2000n≤2000,k≤2000.

对于 100%100\%100% 的数据，1≤n≤500 000,1≤k≤500 0001 \le n \le 500\ 000,1 \le k \le 500\ 0001≤n≤500 000,1≤k≤500 000.

#include<bits/stdc++.h>
#define ll long long
#define A 600000
using namespace std;
ll head[A],nxt[A],belong[A],ver[A],tot=0,deep[A],dis[A],t,n,m,dfn[A],sta[A],otp=0,num=0,top=0,low[A],f[A][30],cnt=0,ins[A],sum[A],rt[A],bl[A],zuzong[A],fa[A],bl4[A];
vector <ll> scc[251001];
bool flag[A];
void add(ll x,ll y)
{nxt[++tot]=head[x];ver[tot]=y;head[x]=tot;}
inline ll lca(ll x,ll y)
{if(deep[x]>deep[y])swap(x,y);for(ll i=t;i>=0;i--){if(deep[x]==deep[y]) break;if(deep[x]<=deep[f[y][i]]) y=f[y][i];}if(x==y) return x;for(ll i=t;i>=0;i--)if(f[x][i]!=f[y][i])x=f[x][i],y=f[y][i];return f[x][0];
}
void dfs(ll x,ll st,ll t)
{deep[x]=st,flag[x]=1;bl4[x]=otp;for(ll i=head[x];i;i=nxt[i]){ll y=ver[i];if(flag[y]) continue;rt[y]=t;dis[y]=dis[x]+1;f[y][0]=x;dfs(y,st+1,t);}return ;
}
ll read()
{ll f=1,x=0;char c=getchar();while(!isdigit(c)){if(c=='-') f=-1;c=getchar();}while(isdigit(c)){x=(x<<1)+(x<<3)+c-'0';c=getchar();}return f*x;
}
inline void tarjan(ll x)
{dfn[x]=low[x]=++num;sta[++top]=x;ins[x]=1;for(ll i=head[x];i;i=nxt[i]){ll y=ver[i];if(dfn[y]==0){tarjan(y);low[x]=min(low[x],low[y]);}else if(ins[y])low[x]=min(low[x],dfn[y]);}if(dfn[x]==low[x]){++cnt;ll yy=0,cis=0,lu;while(1){yy=sta[top--];ins[yy]=0;cis++;    bl4[yy]=cnt;if(yy==x)break;scc[cnt].push_back(yy);belong[yy]=-1;//printf("将%lld赋成-1\n",yy);
}if(cis>1) scc[cnt].push_back(x),belong[x]=-1;else cnt--;}
}
void tiaotarjan()
{cout<<"***"<<endl;for(ll i=1;i<=cnt;i++){for(ll j=0;j<scc[i].size();j++){cout<<scc[i][j]<<" ";}if(scc[i].size()) cout<<endl;}        cout<<"***"<<endl;
}
void tiaos()
{
}
void work()
{n=read();m=read();t=log(n)/log(2)+2;for(ll i=1;i<=n;i++){ll xx=read();add(xx,i);//建反图跑tarjan缩点+lca
    }for(ll i=1;i<=n;i++)if(!dfn[i])    tarjan(i);top=0;memset(flag,0,sizeof(flag));for(ll i=1;i<=cnt;i++){ll size=scc[i].size();otp++;for(ll ii=0;ii<size;ii++){ll q=scc[i][ii]; for(ll j=head[q];j;j=nxt[j]){ll y=ver[j];if(belong[y]!=-1){rt[y]=q;dfs(y,1,rt[y]);f[y][0]=y;}}}}for(ll j=1;j<=t;j++)for(ll i=1;i<=n;i++)f[i][j]=f[f[i][j-1]][j-1];/*for(ll i=1;i<=n;i++){if(belong[i]!=-1){printf("i=%lld rt=%lld deep=%lld\n",i,rt[i],deep[i]);}}*/for(ll i=1;i<=m;i++){    ll xx=read(),yy=read();if(bl4[xx]==bl4[yy]){ll lc=lca(xx,yy);//printf("rtx=%lld rty=%lld\n",rt[xx],rt[yy]);if(rt[xx]==rt[yy]){printf("%lld %lld\n",dis[xx]-dis[lc],dis[yy]-dis[lc]);}if(rt[xx]!=rt[yy]){ll de1=deep[xx],de2=deep[yy];ll now=bl4[rt[xx]];ll size=scc[now].size(),ott=0;bool kais=0;for(ll ii=0;ii<size*2-1;ii++){    if(ii>size){ll j=ii-size;if(!kais&&(scc[now][ii]==rt[xx]||scc[now][ii]==rt[yy])){kais=1;}else if(kais==1){de1<de2?de1++:de2++;if(scc[now][ii]==rt[xx]||scc[now][ii]==rt[yy]){kais=0;break;}}}else{if(!kais&&(scc[now][ii]==rt[xx]||scc[now][ii]==rt[yy])){kais=1;}else if(kais==1){de1<de2?de1++:de2++;if(scc[now][ii]==rt[xx]||scc[now][ii]==rt[yy]){kais=0;break;}}}}printf("%lld %lld\n",de1,de2);}}elseprintf("-1 -1\n");}
}
int main()
{work();}

#include<bits/stdc++.h>
#define ll int
#define A 510000
const int L=1<<20|1;
char buffer[L],*S,*T;
#define getchar() ((S==T&&(T=(S=buffer)+fread(buffer,1,L,stdin),S==T))?EOF:*S++)
using namespace std;
ll head[A],nxt[A],belong[A],ver[A],tot=0,deep[A],t,n,m,otp=0,num=0,f[A][22],cnt=0,bl[A],ances[A],last,sz[A],v[A],cixu[A],chushi=0;
inline ll find(ll x)
{if(ances[x]==x) return x;return ances[x]=find(ances[x]);}
inline void add(ll x,ll y)
{nxt[++tot]=head[x];ver[tot]=y;head[x]=tot;}
inline ll lca(ll x,ll y)
{if(deep[x]>deep[y])swap(x,y);ll w;for(w=0;(1<<w)<=deep[y];w++);w--;for(ll i=w;i>=0;i--){if(deep[x]==deep[y]) break;if(deep[x]<=deep[f[y][i]]) y=f[y][i];}if(x==y) return x;for(ll i=t;i>=0;i--)if(f[x][i]!=f[y][i])x=f[x][i],y=f[y][i];return f[x][0];
}
inline void dfs(ll x,ll pre)
{v[x]=++num;deep[x]=deep[pre]+1;
//    printf("%lld \n",deep[x]);for(ll i=1;(1<<i)<=deep[x];i++)f[x][i]=f[f[x][i-1]][i-1];for(ll i=head[x];i;i=nxt[i]){ll y=ver[i];if(v[y]>last){cnt++;chushi=0;cixu[x]=++chushi;sz[cnt]++;belong[x]=cnt;ances[x]=x;for(ll i=x;i!=y;i=f[i][0]){cixu[f[i][0]]=++chushi;belong[f[i][0]]=cnt;ances[f[i][0]]=f[i][0];sz[cnt]++;}}else {ances[y]=f[y][0]=x,dfs(y,x);}}
}
inline ll Read(){register ll ret;register char r;while(r=getchar(),r<'0'||r>'9');ret=r-48;while(r=getchar(),r>='0'&&r<='9')ret=ret*10+r-48;return ret;
}
inline void work()
{last=0;n=Read();m=Read();t=log(n)/log(2)+1;for(ll i=1;i<=n;i++){ll xx=Read();add(xx,i);}for(ll i=1;i<=n;i++)if(!v[i]){ances[i]=f[i][0]=i;dfs(i,0);last=num;}for(ll i=1;i<=m;i++){    ll x=Read(),y=Read();if(find(x)!=find(y)&&belong[ances[x]]!=belong[ances[y]]) printf("-1 -1\n");else{if(ances[x]==ances[y]){ll lc=lca(x,y);printf("%d %d\n",deep[x]-deep[lc],deep[y]-deep[lc]);}else{ll lx,ly,bl=belong[ances[x]],disx=deep[x]-deep[ances[x]],disy=deep[y]-deep[ances[y]],xy,yx;lx=cixu[ances[x]];ly=cixu[ances[y]];if(lx<ly)xy=ly-lx,yx=sz[bl]-(ly-lx);else yx=lx-ly,xy=sz[bl]-(lx-ly);if(max(disx+xy,disy)<max(disx,disy+yx)) printf("%d %d\n",disx+xy,disy);else if(max(disx+xy,disy)>max(disx,disy+yx)) printf("%d %d\n",disx,disy+yx);else{if(min(disx+xy,disy)<min(disx,disy+yx)) printf("%d %d\n",disx+xy,disy);else if(min(disx+xy,disy)>min(disx,disy+yx)) printf("%d %d\n",disx,disy+yx);else if(disx+xy>=disy) printf("%d %d\n",disx+xy,disy);else printf("%d %d\n",disx,disy+yx);}}}}
}
main()
{work();}

#include<bits/stdc++.h>
#define ll int
#define A 510000
const int L=1<<20|1;
char buffer[L],*S,*T;
#define getchar() ((S==T&&(T=(S=buffer)+fread(buffer,1,L,stdin),S==T))?EOF:*S++)
using namespace std;
ll head[A],nxt[A],belong[A],ver[A],tot=0,deep[A],t,n,m,otp=0,num=0,f[A][22],cnt=0,bl[A],ances[A],last,sz[A],v[A],cixu[A],chushi=0;
inline ll find(ll x)
{if(ances[x]==x) return x;return ances[x]=find(ances[x]);}
inline void add(ll x,ll y)
{nxt[++tot]=head[x];ver[tot]=y;head[x]=tot;}
inline ll lca(ll x,ll y)
{if(deep[x]>deep[y])swap(x,y);ll w;for(w=0;(1<<w)<=deep[y];w++);w--;for(ll i=w;i>=0;i--){if(deep[x]==deep[y]) break;if(deep[x]<=deep[f[y][i]]) y=f[y][i];}if(x==y) return x;for(ll i=t;i>=0;i--)if(f[x][i]!=f[y][i])x=f[x][i],y=f[y][i];return f[x][0];
}
inline void dfs(ll x,ll pre)
{v[x]=++num;deep[x]=deep[pre]+1;
//    printf("%lld \n",deep[x]);for(ll i=1;(1<<i)<=deep[x];i++)f[x][i]=f[f[x][i-1]][i-1];for(ll i=head[x];i;i=nxt[i]){ll y=ver[i];if(v[y]>last){cnt++;chushi=0;cixu[x]=++chushi;sz[cnt]++;belong[x]=cnt;ances[x]=x;for(ll i=x;i!=y;i=f[i][0]){cixu[f[i][0]]=++chushi;belong[f[i][0]]=cnt;ances[f[i][0]]=f[i][0];sz[cnt]++;}}else {ances[y]=f[y][0]=x,dfs(y,x);}}
}
inline ll Read(){register ll ret;register char r;while(r=getchar(),r<'0'||r>'9');ret=r-48;while(r=getchar(),r>='0'&&r<='9')ret=ret*10+r-48;return ret;
}
inline void work()
{last=0;n=Read();m=Read();t=log(n)/log(2)+1;for(ll i=1;i<=n;i++){ll xx=Read();add(xx,i);}for(ll i=1;i<=n;i++)if(!v[i]){ances[i]=f[i][0]=i;dfs(i,0);last=num;}for(ll i=1;i<=m;i++){    ll x=Read(),y=Read();if(find(x)!=find(y)&&belong[ances[x]]!=belong[ances[y]]) printf("-1 -1\n");else{if(ances[x]==ances[y]){ll lc=lca(x,y);printf("%d %d\n",deep[x]-deep[lc],deep[y]-deep[lc]);}else{ll lx,ly,bl=belong[ances[x]],disx=deep[x]-deep[ances[x]],disy=deep[y]-deep[ances[y]],xy,yx;lx=cixu[ances[x]];ly=cixu[ances[y]];if(lx<ly)xy=ly-lx,yx=sz[bl]-(ly-lx);else yx=lx-ly,xy=sz[bl]-(lx-ly);if(max(disx+xy,disy)<max(disx,disy+yx)) printf("%d %d\n",disx+xy,disy);else if(max(disx+xy,disy)>max(disx,disy+yx)) printf("%d %d\n",disx,disy+yx);else{if(min(disx+xy,disy)<min(disx,disy+yx)) printf("%d %d\n",disx+xy,disy);else if(min(disx+xy,disy)>min(disx,disy+yx)) printf("%d %d\n",disx,disy+yx);else if(disx+xy>=disy) printf("%d %d\n",disx+xy,disy);else printf("%d %d\n",disx,disy+yx);}}}}
}
main()
{work();}