#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
typedef long long ll;
using namespace __gnu_pbds;
using namespace std;
#define ff first
#define ss second
#define pi pair<ll, ll>
#define pll pair<long long, long long>
#define vi vector<ll>
#define vll vector<long long>
#define vpi vector<pair<ll,ll>>
#define vpll vector<pair<long long, long long>>
#define pb push_back
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define sz(x) (ll)(x).size()
#define forall(it,x) for(auto& it:(x))
#define mp make_pair
pi operator+(pi a, pi b) { return mp(a.ff+b.ff, a.ss+b.ss); }
pi operator-(pi a, pi b) { return mp(a.ff-b.ff, a.ss-b.ss); }
template <typename T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
ll base = 1<<20;
struct SegTree {
vector<ll> T;
SegTree() {
T.assign(2*base, 1e9);
}
void update(ll a, ll b, ll val) {
if(a>b)return;
if(a==b) {
T[a+base] = min(T[a+base], val);
return;
}
a+=base-1;
b+=base+1;
while(a/2 != b/2) {
if(a%2==0) T[a+1] = min(T[a+1], val);
if(b%2==1) T[b-1] = min(T[b-1], val);
a/=2; b/=2;
}
}
ll query(ll x) {
ll res = 1e9;
x+=base;
while(x > 0) {
res = min(res, T[x]);
x/=2;
}
return res;
}
};
signed main() {
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
ll n, q, K;
cin >> n >> q >> K;
vector<ll> A(n+1);
for(ll i=1; i<=n; ++i) cin >> A[i];
for(ll i=2; i<=n; i+=2) A[i] *= -1;
vector<ll> P(n+1);
for(ll i=1; i<=n; ++i) P[i] = P[i-1] + A[i];
vector<ll> rem;
for(ll i=1; i<=n; ++i) rem.pb(((P[i-1]%K)+K)%K);
sort(all(rem));
rem.erase(unique(all(rem)), rem.end());
vector<ll> nxt(n+1, n+1);
SegTree st;
for(ll i=n; i>=1; --i) {
if(A[i] <= -K) st.update(0, base-1, i);
else if(A[i] < 0) {
ll pp = ((P[i-1]%K)+K)%K;
ll L = upper_bound(all(rem), pp + A[i]) - rem.begin();
ll R = upper_bound(all(rem), pp) - rem.begin() - 1;
st.update(L,R,i);
L = upper_bound(all(rem), max(pp, pp + A[i] + K)) - rem.begin();
st.update(L,base-1,i);
for(ll j=0; j<(ll)rem.size(); ++j) {
if(pp >= rem[j]) {
if(rem[j] > pp + A[i]) st.update(j,j,i);
} else {
if(rem[j] > pp + A[i] + K) st.update(j,j,i);
}
}
}
ll idx = lower_bound(rem.begin(), rem.end(), ((P[i-1]%K)+K)%K) - rem.begin();
nxt[i] = min(nxt[i], st.query(idx));
}
// for(ll i=1; i<=n; ++i) cout << nxt[i] << " ";
// cout << "\n";
ll maxlog = 20;
vector<vector<pair<ll, ll>>> jump(n+1, vector<pi>(maxlog+1, {n+5, 0}));
for(ll i=1; i<=n; ++i) {
jump[i][0] = {nxt[i]+1, (P[nxt[i]-1] - P[i-1]) / K};
}
for(ll j=1; j<=maxlog; ++j) {
for(ll i=1; i<=n; ++i) {
if(jump[i][j-1].first > n) continue;
jump[i][j].first = jump[jump[i][j-1].first][j-1].first;
jump[i][j].second = jump[i][j-1].second + jump[jump[i][j-1].first][j-1].second;
}
}
while(q--) {
ll l, r;
cin >> l >> r;
if(A[l] < 0) l++;
if(l > r) {
cout << "0\n";
continue;
}
ll res = 0;
for(ll j=maxlog; j>=0; --j) {
if(l > n) break;
if(jump[l][j].first-1 <= r) {
res += jump[l][j].second;
l = jump[l][j].first;
}
}
res += (P[r] - P[l-1]) / K;
cout << res << "\n";
}
return 0;
}
