#include<bits/stdc++.h>
#define int long long
using namespace std;
int a[200005];
int n,q,t;
struct node{
node *l,*r;
int info;
int lz=0;
node(int x=0){
info=x;
l=r=NULL;
}
};
typedef node* pnode;
struct psegtree{
pnode rt[200005];
void push(int st,int en,pnode &x){
if(x->lz==0)return;
x->info+=x->lz;
if(st!=en){
x->l->lz+=x->lz;
x->r->lz+=x->lz;
}
x->lz=0;
}
void build(int st,int en,pnode &x){
x=new node();
if(st==en){
return void(x->info=st);
}
int m=(st+en)/2;
build(st,m,x->l);
build(m+1,en,x->r);
x->info=max(x->l->info,x->r->info);
}
void upd(int st,int en,pnode x,pnode &y,int l,int r,int val){
//cerr<<"try:"<<st<<" "<<en<<"\n";
y=new node(*x);
if(st>r||en<l)return;
if(st>=l&&en<=r){
y->lz+=val;
return;
}
int m=(st+en)/2;
upd(st,m,x->l,y->l,l,r,val);
upd(m+1,en,x->r,y->r,l,r,val);
y->info=max(y->l->info+y->l->lz,y->r->info+y->r->lz);
}
int fval(int st,int en,pnode &x,int pos,int sum=0){
int m=(st+en)/2;
sum+=x->lz;
if(st==en)return x->info+sum;
if(pos<=m)return fval(st,m,x->l,pos,sum);
else return fval(m+1,en,x->r,pos,sum);
}
int f(int st,int en,pnode &x,int val){
val-=x->lz;
if(st==en)return st;
int m=(st+en)/2;
if(x->l->info+x->l->lz<=val)return f(m+1,en,x->r,val);
else return f(st,m,x->l,val);
}
}tr;
pair<int,int> lca(int x,int lx,int y,int ly){
if(lx<ly){
swap(x,y);
swap(lx,ly);
}
for(int i=19;i>=0;i--){
if(lx-(1<<i)>=ly)lx-=(1<<i);
}
//if(p[lx][x]==p[ly][y])return {x,lx};
if(tr.fval(1,n+1,tr.rt[lx],x)==tr.fval(1,n+1,tr.rt[ly],y))return {x,lx};
for(int i=19;i>=0;i--){
if(lx-(1<<i)>0){
//p[lx-(1<<i)][x]!=p[ly-(1<<i)][y]
if(tr.fval(1,n+1,tr.rt[lx-(1<<i)],x)!=tr.fval(1,n+1,tr.rt[ly-(1<<i)],y)){
lx=lx-(1<<i),ly=ly-(1<<i);
}
}
}
return make_pair(x,lx-1);
}
int32_t main(){
ios_base::sync_with_stdio(false);
cin.tie(0);
cin>>n>>q>>t;
for(int i=1;i<=n;i++){
cin>>a[i];
}
//cerr<<"work\n";
tr.build(1,n+1,tr.rt[n+1]);
for(int i=n;i>=1;i--){
int x=a[i]-(i*(i-1)/2);
//cerr<<"i:"<<i<<" "<<x<<"\n";
//int pos=upper_bound(p[i+1]+1,p[i+1]+1+n,x)-p[i+1];
int pos=tr.f(1,n+1,tr.rt[i+1],x);
//cerr<<"pos:"<<pos<<"\n";
//for(int j=1;j<=n+1;j++)p[i][j]=p[i+1][j];
//for(int j=pos;j<=n+1;j++)p[i][j]--;
tr.upd(1,n+1,tr.rt[i+1],tr.rt[i],pos,n+1,-1);
//cerr<<"upd\n";
/*for(int k=i;k<=n+1;k++){
for(int j=1;j<=n+1;j++){
cerr<<tr.fval(1,n+1,tr.rt[k],j)<<" ";
}
cerr<<"\n";
}
cerr<<"\n";*/
}
/*cerr<<"\n";
for(int i=1;i<=n+1;i++){
for(int j=1;j<=n+1;j++){
cerr<<tr.fval(1,n+1,tr.rt[i],j)<<" ";
}
cerr<<"\n";
}
cerr<<"work\n";*/
int prv=0;
int md=(n+1)*(n+2)/2;
vector<int>st;
for(int i=1;i<=n+1;i++){
st.push_back(i*(i-1)/2+1);
}
for(int i=0;i<q;i++){
int x,y;cin>>x>>y;
x=(x-1+t*prv)%(md)+1;
y=(y-1+t*prv)%(md)+1;
int lx=upper_bound(st.begin(),st.end(),x)-st.begin();
int ly=upper_bound(st.begin(),st.end(),y)-st.begin();
x-=(lx*(lx-1)/2);
y-=(ly*(ly-1)/2);
/*
x=lower_bound(p[lx]+1,p[lx]+n+2,x)-p[lx];
y=lower_bound(p[ly]+1,p[ly]+n+2,y)-p[ly];*/
x=tr.f(1,n+1,tr.rt[lx],x-1);
y=tr.f(1,n+1,tr.rt[ly],y-1);
auto ans=lca(x,lx,y,ly);
//int rans=p[ans.second][ans.first]+ans.second*(ans.second-1)/2;
int rans=tr.fval(1,n+1,tr.rt[ans.second],ans.first)+ans.second*(ans.second-1)/2;
cout<<rans<<"\n";
prv=rans;
}
}
