#include <bits/stdc++.h>
#include <cassert>
#pragma GCC optimize("O3")
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
using namespace std;
using ll = long long;
ll n,Q,k;
ll ar[500002];
ll s[500002];
ll sp[500002];
int nxt[500002];
vector<ll> comp;
int seg[4000002];
vector<int> inv[1500002];
vector<int> outv[1500002];
vector<int> pv[1500002];
int d[500002][22];
ll sd[500002][22];
int Upd(int node, int nL, int nR, int idx, int val){
if(nL>idx || nR<idx)return seg[node];
if(nL==nR)return seg[node] = min(seg[node],val);
int mid = (nL+nR)/2;
return seg[node] = min(Upd(node*2,nL,mid,idx,val),Upd(node*2+1,mid+1,nR,idx,val));
}
int Query(int node, int nL, int nR, int l, int r){
if(nL>r || nR<l)return n;
if(l<=nL && nR<=r)return seg[node];
int mid = (nL+nR)/2;
return min(Query(node*2,nL,mid,l,r),Query(node*2+1,mid+1,nR,l,r));
}
int ii(ll x){
return lower_bound(comp.begin(),comp.end(),x)-comp.begin();
}
int main(){
ios::sync_with_stdio(0);
cin.tie(0);
cin>>n>>Q>>k;
for(int i=1;i<=n;i++)cin>>ar[i];
for(int i=1;i<=n;i++){
if(i%2==1)s[i] = s[i-1]+ar[i];
else s[i] = s[i-1]-ar[i];
}
for(int i=1;i<=n;i++)sp[i] = s[i]%k;
for(int i=1;i<=n;i++)if(sp[i]<0)sp[i]+=k;
/* for(int i=1;i<=n;i++){
if(i%2==1){
nxt[i] = n+1;
for(int j=i+1;j<=n;j+=2){
if(k-sp[i-1]<=ar[j]-sp[j-1] || (sp[j-1]-ar[j]<=sp[i-1] && sp[i-1]<=sp[j-1])){
nxt[i] = j+1;
break;
}
}
cout<<nxt[i];
}
}*/
for(int i=1;i<=n;i++){
comp.push_back(ar[i]-sp[i-1]);
comp.push_back(k-sp[i-1]);
}
comp.push_back(k-sp[n]);
for(int i=0;i<=4e6;i++)seg[i] = n;
sort(comp.begin(),comp.end());
comp.erase(unique(comp.begin(),comp.end()),comp.end());
for(int i=n;i>=1;i--){
if(i%2==0){
Upd(1,0,2*n,ii(ar[i]-sp[i-1]),i);
}
else{
nxt[i] = Query(1,0,2*n,ii(k-sp[i-1]),2*n)+1;
}
}
comp.clear();
for(int i=1;i<=n;i++){
comp.push_back(sp[i-1]-ar[i]);
comp.push_back(sp[i-1]);
comp.push_back(sp[i-1]+1);
}
sort(comp.begin(),comp.end());
comp.erase(unique(comp.begin(),comp.end()),comp.end());
for(int i=1;i<=n;i+=2){
pv[ii(sp[i-1])].push_back(i);
}
for(int i=2;i<=n;i+=2){
inv[ii(sp[i-1]-ar[i])].push_back(i);
outv[ii(sp[i-1]+1)].push_back(i);
}
set<int> ss;
ss.insert(n+1);
for(int i=0;i<comp.size();i++){
for(int ele:inv[i]){
ss.insert(ele);
}
for(int ele:outv[i])ss.erase(ele);
for(int ele:pv[i]){
nxt[ele] = min(nxt[ele],*(ss.lower_bound(ele))+1);
}
}
/* for(int i=1;i<=n;i+=2)cout<<nxt[i];*/
nxt[n+1] = n+1;
for(int i=1;i<=n+1;i++){
d[i][0] = nxt[i];
sd[i][0] = max((ll)0,s[nxt[i]-2]-s[i-1])/k;
}
for(int i=1;i<20;i++){
for(int j=1;j<=n+1;j++){
d[j][i] = d[d[j][i-1]][i-1];
sd[j][i] = sd[j][i-1]+sd[d[j][i-1]][i-1];
}
}
while(Q--){
int l,r;
cin>>l>>r;
if(l%2==0)l++;
if(r%2==0)r--;
if(l>r){
cout<<0<<'\n';
continue;
}
/*int cur = l;
ll ans = 0;
while(true){
int nc = nxt[cur];
if(nc<=r)ans+=(s[nc-2]-s[cur-1])/k;
else{
ans+=(s[r]-s[cur-1])/k;
break;
}
cur = nc;
}*/
ll ans = 0;
int cur = l;
for(int i=19;i>=0;i--){
if(d[cur][i]<=r){
ans += sd[cur][i];
cur = d[cur][i];
}
}
ans+=(s[r]-s[cur-1])/k;
cout<<ans<<'\n';
}
return 0;
}
