#include<cstdio>
#include<algorithm>
#include<cmath>
#define N 41451
using namespace std;
int tot,k,n,m,block,left[100],right[100],pos[N],cnt[50][50][N],f[50][50],num[50][50];
int a[N],b[N];
void lsh(int *a,int n){
	for(int i=1;i<=n;i++)b[i]=a[i];
	sort(b+1,b+n+1);k=unique(b+1,b+n+1)-b-1;
	for(int i=1;i<=n;i++)a[i]=lower_bound(b+1,b+k+1,a[i])-b;
}
void build(){
	block=(int)pow(1.0*n,2.0/3);
	tot=n/block;
	if(n%block)tot++;
	for(int i=1;i<=n;i++)scanf("%d",&a[i]),pos[i]=(i-1)/block+1;
	lsh(a,n);
	for(int i=1;i<=tot;i++){
		left[i]=(i-1)*block+1;
		right[i]=i*block;
	}
	right[tot]=n;
	for(int i=1;i<=tot;i++){
		for(int j=i;j<=tot;j++){
			for(int t=left[i];t<=right[j];t++)cnt[i][j][a[t]]++;
			for(int t=1;t<=k;t++){
				if(cnt[i][j][t]>f[i][j]||(cnt[i][j][t]==f[i][j]&&t<num[i][j])){
					f[i][j]=cnt[i][j][t];
					num[i][j]=t;
				}
			}
		}
	} 
}
int query(int l,int r){
	int le=pos[l]+1,ri=pos[r]-1;
	if(le>ri)le=ri=0;
	int res1=f[le][ri],res2=num[le][ri];
	if(pos[l]==pos[r]){
		for(int i=l;i<=r;i++){
			int now=cnt[le][ri][a[i]]+1;
			if(now>res1||(now==res1&&a[i]<res2))res1=now,res2=a[i];
		}
	}else{
		for(int i=l;i<=right[pos[l]];i++){
			int now=cnt[le][ri][a[i]]+1;
			if(now>res1||(now==res1&&a[i]<res2))res1=now,res2=a[i];
		}
		for(int i=left[pos[r]];i<=r;i++){
			int now=cnt[le][ri][a[i]]+1;
			if(now>res1||(now==res1&&a[i]<res2))res1=now,res2=a[i];
		}
	}
	return b[res2];
}
signed main(){
	scanf("%d%d",&n,&m);
	build();
	int las=0;
	while(m--){
		int l,r;
		scanf("%d%d",&l,&r);
		l=(l+las-1)%n+1;
		r=(r+las-1)%n+1;
		if(l>r)swap(l,r);
		printf("%d\n",las=query(l,r)); 
	}
	return 0;
}