#pragma GCC optimize("O3,inline")
#include <bits/stdc++.h>
using namespace std;
#define int long long
set<pair<int, int>> ss;
void upd(int a, int b, int x) {
auto iter1 = ss.lower_bound({ a, 0 });
auto iter2 = ss.upper_bound({ b, 1e15 });
auto iter3 = ss.upper_bound({ b + 1, 1e15 });
iter3--;
int guy = iter3->second;
ss.erase(iter1, iter2);
ss.insert({ a, x });
ss.insert({ b + 1, guy });
}
int qry(int a) {
auto iter = ss.upper_bound({ a, 1e15 });
iter--;
return iter->second;
}
signed main() {
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
int N, Q, K, a, b, crnt = 0; cin >> N >> Q >> K;
vector<int> p = { 0 }, A;
for (int i = 0; i < N; i++) {
cin >> a;
if (i % 2) {
crnt -= a;
A.push_back(-a);
}
else {
crnt += a;
A.push_back(a);
}
p.push_back(crnt);
}
if (N % 2) {
N++;
A.push_back(-1e15);
p.push_back(crnt - 1e15);
}
ss.insert({ 0, N });
vector<vector<pair<int, int>>> kpa(20, vector<pair<int, int>>(N + 1, {N + 1, -1}));
for (int i = N - 1; i >= 0; i--) {
if (i % 2) {
if (A[i] <= -K) upd(0, K - 1, i);
else {
a = ((p[i] + A[i]) % K + K) % K, b = (p[i] % K + K) % K;
if (a <= b) upd(a, b, i);
else {
upd(0, b, i);
upd(a, K - 1, i);
}
}
}
int res = qry((p[i] % K + K) % K);
kpa[0][i] = { res + 1, (p[res] - p[i]) / K };
}
for (int i = 1; i < 20; i++) {
for (int j = 0; j <= N; j++) {
if (kpa[i - 1][j].first == N + 1) continue;
kpa[i][j] = kpa[i - 1][kpa[i - 1][j].first];
kpa[i][j].second += kpa[i - 1][j].second;
}
}
for (int i = 0; i < Q; i++) {
cin >> a >> b; a--;
int res = 0;
for (int j = 19; j >= 0; j--) {
if (kpa[j][a].first > b) continue;
res += kpa[j][a].second;
a = kpa[j][a].first;
}
res += (p[b] - p[a]) / K;
cout << res << '\n';
}
}
