#include<iostream>
#include<cstring>
#include<cstdio>
#include<string>
#include<algorithm>
#include<cmath>
#include<utility>
#include<cstdlib>
#include<iomanip>	//cout<<setiosflags(ios::fixed)<<setprecision(2);
#include<ctime> //double a=(double)clock();	cout<<a<<endl;
#include<vector>
#include<queue>
#include<map>
using namespace std;
const int maxn=40010;
inline int read(){
	int x=0,ff=1;char ch=getchar();
	while(ch>'9'||ch<'0'){if(ch=='-')ff=-1; ch=getchar();}
	while(ch<='9'&&ch>='0'){x=x*10+ch-'0';ch=getchar();}
	return ff*x;
}
inline void myswap(int &xx,int &yy)
{xx^=yy,yy^=xx,xx^=yy;}
int N,M,a[maxn],x,L,R,b[maxn],c[maxn],cnt=0;
int have[maxn],maxx,v,temp;
map<int,int>mp;
inline bool mycmp(const int &A,const int &B)
{return a[A]<a[B];}
void print_for_checking(){
	for(int i=1;i<=N;i++)
		printf("%d ",mp[a[i]]);
	puts("");
	return;
}
void query(){
	maxx=0;
	memset(have,0,sizeof(have));
	for(int i=L;i<=R;i++){
		temp=mp[a[i]];
		have[temp]++;
		if(have[temp]>maxx)
			maxx=have[temp],v=temp;
		else if(have[temp]==maxx)
			if(c[v]>a[i])
				v=temp;
	}
	x=c[v];
	printf("%d\n",x);
}
int main(){
	freopen("numquery.in","r",stdin);
	freopen("numquery.out","w",stdout);
	N=read(),M=read();
	for(int i=1;i<=N;i++)
		a[i]=read(),b[i]=i;
	sort(b+1,b+1+N,mycmp);
	for(int i=1;i<=N;i++)
		if(mp[a[b[i]]]==0)
			mp[a[b[i]]]=++cnt,c[cnt]=a[b[i]];
	//print_for_checking();
	x=0;
	while(M--){
		L=read(),R=read();
		L=(L+x-1)%N+1,R=(R+x-1)%N+1;
		if(L>R)
			myswap(L,R);
		query();
		//printf("%d %d\n",L,R);
	}
	return 0;
}