#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<vector>
using namespace std;
int maxn,m,n,tot,T,mode[1000][1000],last[40010],
a[40010],ord[40010],L[1000],R[1000],cnt[40010];
vector<int> plc[40010];
vector<int>::iterator i1,i2;
int main()
{
    int i,j,k,p,q,x,y,z,K,ans,l,r,ll,rr,ans_cnt,xx;
    scanf("%d%d",&n,&m);
    for (i=1;i<=n;i++)
      scanf("%d",&a[i]),ord[i]=a[i];
    sort(ord+1,ord+n+1);
    maxn=unique(ord+1,ord+n+1)-ord-1;
    for (i=1;i<=n;i++)
      a[i]=lower_bound(ord+1,ord+maxn+1,a[i])-ord;
    tot=sqrt(n*log(n)/log(2));
    T=n/tot;
    for (i=1;i<=tot;i++)
    {
        L[i]=R[i-1]+1;
        if (i==tot) R[i]=n;
        else R[i]=L[i]+T-1;
    }
    for (i=1;i<=tot;i++)
    {
        memset(cnt,0,sizeof(cnt));
        for (j=i;j<=tot;j++)
        {
            mode[i][j]=mode[i][j-1];
            for (k=L[j];k<=R[j];k++)
            {
                cnt[a[k]]++;
                if (cnt[a[k]]>cnt[mode[i][j]]||
                  (cnt[a[k]]==cnt[mode[i][j]]&&a[k]<mode[i][j]))
                    mode[i][j]=a[k];
            }
        }
    }
    for (i=1;i<=n;i++)
      plc[a[i]].push_back(i);
    ans=0;
    for (K=1;K<=m;K++)
    {
        scanf("%d%d",&l,&r);
        l=(l+ans-1)%n+1;
        r=(r+ans-1)%n+1;
        if (l>r) swap(l,r);
        ll=1;
        while (ll<=tot&&L[ll]<l) ll++;
        rr=tot;
        while (rr&&R[rr]>r) rr--;
        if (ll>rr)
        {
            ans=0;
            ans_cnt=-1;
            for (i=l;i<=r;i++)
            {
                i1=lower_bound(plc[a[i]].begin(),plc[a[i]].end(),l);
                i2=upper_bound(plc[a[i]].begin(),plc[a[i]].end(),r);
                xx=i2-i1;
                if (xx>ans_cnt||(xx==ans_cnt&&a[i]<ans))
                {
                    ans=a[i];
                    ans_cnt=xx;
                }
            }
            ans=ord[ans];
            printf("%d\n",ans);
            continue;
        }
        ans=mode[ll][rr];
        i1=lower_bound(plc[ans].begin(),plc[ans].end(),l);
        i2=upper_bound(plc[ans].begin(),plc[ans].end(),r);
        ans_cnt=i2-i1;
        for (i=l;i<L[ll];i++)
        {
            i1=lower_bound(plc[a[i]].begin(),plc[a[i]].end(),l);
            i2=upper_bound(plc[a[i]].begin(),plc[a[i]].end(),r);
            xx=i2-i1;
            if (xx>ans_cnt||(xx==ans_cnt&&a[i]<ans))
            {
                ans=a[i];
                ans_cnt=xx;
            }
        }
        for (i=R[rr]+1;i<=r;i++)
        {
            i1=lower_bound(plc[a[i]].begin(),plc[a[i]].end(),l);
            i2=upper_bound(plc[a[i]].begin(),plc[a[i]].end(),r);
            xx=i2-i1;
            if (xx>ans_cnt||(xx==ans_cnt&&a[i]<ans))
            {
                ans=a[i];
                ans_cnt=xx;
            }
        }
        ans=ord[ans];
        printf("%d\n",ans);
    }
}