#include<cstdio>
#include<algorithm>
#include<iostream>
#include<cstring>
using namespace std;
const int SIZEN=40010;
int a[SIZEN],A[SIZEN];
int tot=0,N,M;
void read()
{
	scanf("%d%d",&N,&M);
	for(int i=1;i<=N;i++)
	{
		scanf("%d",&a[i]);
		A[i]=a[i];
	}
}
/*class miku
{
public:
	int l,r;
	int ls,rs;
	int sum,id;
	miku()
	{
		sum=0;id=0;
	}
	#define l(x) tr[x].l
	#define r(x) tr[x].r
	#define ls(x) tr[x].ls
	#define rs(x) tr[x].rs
	#define sum(x) tr[x].sum
	#define id(x) tr[x].id
}tr[SIZEN*40];
int root[SIZEN];
int built(int l,int r)
{
	int now=++tot;
	l(now)=l;r(now)=r;
	id(now)=l;sum(now)=0;
	if(l<r)
	{
		int mid=(l+r)/2;
		ls(now)=built(l,mid);
		rs(now)=built(mid+1,r);
	}
	return now;
}
int change(int k,int pos,int t)
{
	int now=++tot;
	tr[now]=tr[k];
	if(l(now)==r(now))
	{
		sum(pos)+=t;
		return now;
	}
	int mid=(l(now)+r(now))/2;
	if(pos<=mid) ls(now)=change(ls(now),pos,t);
	else rs(now)=change(rs(now),pos,t);
	return now;
}*/
void prepare()
{
	sort(A+1,A+1+N);
	int n=1;
	for(int i=2;i<=N;i++) if(A[i]!=A[i-1]) A[++n]=A[i];
	for(int i=1;i<=N;i++) a[i]=lower_bound(A+1,A+1+n,a[i])-A;
}
int ans=0;
int cnt[SIZEN]={0};
void Calc(int L,int R)
{
	int now=0;
	for(int i=L;i<=R;i++)
	{
		cnt[a[i]]++;
		if(cnt[a[i]]>cnt[now]||a[i]<now)
		{
			ans=A[a[i]];
			now=a[i];
		}
		//cout<<now<<endl;
	}
	for(int i=L;i<=R;i++) cnt[a[i]]--;
	printf("%d\n",ans);
}
void work()
{
	int L,R;
	//cout<<N<<" "<<M<<endl;
	for(int i=1;i<=M;i++)
	{
		scanf("%d%d",&L,&R);
		L=(L+ans-1)%N+1;R=(R+ans-1)%N+1;
		if(R<L) swap(L,R);
		//cout<<L<<" "<<R<<endl;
		Calc(L,R);
		//ans=query(root[R],root[L-1]);
	}
}
int main()
{
	freopen("numquery.in","r",stdin);
	freopen("numquery.out","w",stdout);
	read();
	prepare();
	work();
	return 0;
}