/*
Language: c++
Author: lxtgogogo
Date: 2016.04.15
没关系我还有一个小时。。。
一个小时敲一道数据结构题？Naive!!!
*/
#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<iomanip>
#include<queue>
using namespace std;
inline int read(){
	int x=0;bool f=true;char ch=getchar();
	while(ch>'9' || ch<'0')	{if(ch=='-'){f=false;}ch=getchar();}
	while(ch>='0' && ch<='9')	{x=(x<<1)+(x<<3)+ch-'0';ch=getchar();}
	return f?x:-x;
}
const int NN=40010;
const int MM=50010;
int n=0,m=0,ans;
int L0[MM]={},R0[MM]={};
int x=0,y=0;
int maxx[3005][3005]={};
int hash[NN]={};
int f[3005]={};

struct haha{
	int num,id,h;
}a[NN];

bool mycmp(haha a,haha b){return a.num<b.num;}
bool mycmp2(haha a,haha b){return a.id<b.id;}
void init(){
	n=read();m=read();
	for(int i=1;i<=n;i++)	{a[i].num=read();a[i].id=i;}
	for(int i=1;i<=m;i++)	{L0[i]=read();R0[i]=read();}
}
void first(){
	sort(a+1,a+n+1,mycmp);
	int ge=0;
	for(int i=1;i<=n;i++)
	{
		if(a[i].num!=a[i-1].num)	{ge++;hash[ge]=a[i].num;}
		a[i].h=ge;
	}
	sort(a+1,a+n+1,mycmp2);
	for(int i=1;i<=n;i++)
	{
		memset(f,0,sizeof(f));
		int temp=i;
		for(int j=i;j<=n;j++)
		{
			f[a[j].h]++;
			if(f[a[j].h]>f[temp] || (f[a[j].h]==f[temp] && a[j].num<a[temp].num))	temp=j;
			maxx[i][j]=a[temp].num;
		}
	}
}
int main(){
	freopen("numquery.in","r",stdin);
	freopen("numquery.out","w",stdout);
	
	init();
	first();
	for(int i=1;i<=m;i++)
	{
		x=(L0[i]+ans-1)%n+1;
		y=(R0[i]+ans-1)%n+1;
		if(x>y)	swap(x,y);
		ans=maxx[x][y];
		printf("%d\n",ans);
	}
	
	fclose(stdin);fclose(stdout);
	return 0;
}