#include<iostream>

 #include<cstring>

 #include<cmath>

 #include<cstdio>

 #include<algorithm>

 #include<vector>

 using namespace std;

 const int N=;

 vector<int> vec[N];

 int n,m,a[N],b[N],block[N],ans,Block,L[N],R[N],cnt[N],top,stack[N],f[][],ff[][],tot;

 int find1(int x,int y){

     int l=;int r=vec[x].size()-;

     int tmp=-;

     while(l<=r){

         int mid=(l+r)>>;

         if(vec[x][mid]<=y){

             tmp=mid;

             l=mid+;

         }

         else r=mid-;

     }

     return tmp;

 }

 int find2(int x,int y){

     int l=;int r=vec[x].size()-;

     int tmp=;

     while(l<=r){

         int mid=(l+r)>>;

         if(vec[x][mid]>=y){

             tmp=mid;

             r=mid-;

         }

         else l=mid+;

     }

     return tmp;

 }

 int main(){

     scanf("%d%d",&n,&m);

     Block=sqrt(n);

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

         scanf("%d",&a[i]);

         b[i]=a[i];

     }

     sort(b+,b++n);

     int num=unique(b+,b++n)-b-;

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

         a[i]=lower_bound(b+,b++num,a[i])-b;

         block[i]=(i-)/Block+;

         vec[a[i]].push_back(i);

         if(!L[block[i]])L[block[i]]=i;

         R[block[i]]=i;

     }

     for(int i=;i<=block[n];i++){

         tot=;

         for(int j=L[i];j<=n;j++){

             cnt[a[j]]++;

             if(tot<=cnt[a[j]]){

                 if(cnt[a[j]]>tot)ans=b[a[j]];

                 else ans=min(ans,b[a[j]]);

                 tot=cnt[a[j]];

             }

             f[i][block[j]]=tot;

             ff[i][block[j]]=ans;

         }

         for(int j=L[i];j<=n;j++){

             cnt[a[j]]=;

         }

     }

     ans=;

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

         int l,r;

         scanf("%d%d",&l,&r);

         l=(l+ans-)%n+;r=(r+ans-)%n+;

         if(l>r)swap(l,r);

         if(block[l]+>=block[r]){

             tot=;

             ans=;

             for(int i=l;i<=r;i++){

                 cnt[a[i]]++;

                 if(tot<=cnt[a[i]]){

                     if(cnt[a[i]]>tot)ans=b[a[i]];

                     else ans=min(ans,b[a[i]]);

                     tot=cnt[a[i]];

                 }

             }

             for(int i=l;i<=r;i++){

                 cnt[a[i]]=;

             }

         }

         else{

             top=;

             tot=f[block[l]+][block[r]-];

             ans=ff[block[l]+][block[r]-];

             for(int i=l;i<=R[block[l]];i++){

                 cnt[a[i]]++;

                 if(cnt[a[i]]==)stack[++top]=a[i];

             }

             for(int i=L[block[r]];i<=r;i++){

                 cnt[a[i]]++;

                 if(cnt[a[i]]==)stack[++top]=a[i];

             }

             while(top){

                 int z=stack[top--];

                 int tmp=max(,find1(z,L[block[r]]-)-find2(z,R[block[l]]+)+);

                 if(tot<=cnt[z]+tmp){

                     if(cnt[z]+tmp>tot)ans=b[z];

                     else ans=min(ans,b[z]);

                     tot=cnt[z]+tmp;

                 }

                 cnt[z]=;

             }

         }

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

     }

     return ;

 }