#include <bits/stdc++.h>
#ifndef LOCAL
#include "meetings.h"
#endif
using namespace std;
#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define all(a) (a).begin(), (a).end()
#define Time (clock() * 1.0 / CLOCKS_PER_SEC)
using ll = long long;
using ull = unsigned long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
using ld = long double;
template<typename T1, typename T2> bool chkmin(T1& x, T2 y) {
return y < x ? (x = y, true) : false;
}
template<typename T1, typename T2> bool chkmax(T1& x, T2 y) {
return y > x ? (x = y, true) : false;
}
void debug_out() {
cerr << endl;
}
template<typename T1, typename... T2> void debug_out(T1 A, T2... B) {
cerr << ' ' << A;
debug_out(B...);
}
template<typename T> void mdebug_out(T* a, int n) {
for (int i = 0; i < n; ++i)
cerr << a[i] << ' ';
cerr << endl;
}
#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define mdebug(a, n) cerr << #a << ": ", mdebug_out(a, n)
#else
#define debug(...) 1337
#define mdebug(a, n) 1337
#endif
template<typename T> ostream& operator << (ostream& stream, const vector<T>& v) {
for (auto& x : v)
stream << x << ' ';
return stream;
}
template<typename T1, typename T2> ostream& operator << (ostream& stream, const pair<T1, T2>& p) {
return stream << p.first << ' ' << p.second;
}
template<typename T> ostream& operator << (ostream& stream, const deque<T>& v) {
for (auto& x : v)
stream << x << ' ';
return stream;
}
#ifdef LOCAL
mt19937 rng(1337);
#else
mt19937 rng(time(0));
#endif
const int INF32 = 1e9;
const ll INF64 = 1e18;
const int maxN = 750005;
int n, Q;
int a[maxN];
int randY[maxN], irandY[maxN];
vector<int> que[maxN];
namespace sgt {
const int logN = 20;
const int N = 1 << logN;
pii t[2 * N];
void build(bool rev = false) {
for (int i = 0; i < n; ++i)
t[i + N] = (!rev ? mp(a[i], randY[i]) : mp(a[i], randY[i]));
for (int i = N - 1; i >= 1; --i) {
t[i] = max(t[i << 1], t[i << 1 | 1]);
}
}
int argmax(int l, int r) {
pii ans = {-INF32, -INF32};
for (l += N, r += N; l <= r; l >>= 1, r >>= 1) {
if (l & 1) chkmax(ans, t[l++]);
if (~r & 1) chkmax(ans, t[r--]);
}
return irandY[ans.se];
}
}
struct line {
int k;
ll b;
line() {}
line(ll _k, ll _b): k(_k), b(_b) {}
ll f(ll x) {
return k * x + b;
}
};
ostream& operator << (ostream& stream, const line& l) {
return stream << l.k << "i + " << l.b;
}
double intersect(const line& lhs, const line& rhs) {
return (rhs.b - lhs.b) / (double)(lhs.k - rhs.k);
}
namespace treap {
struct Node {
int y, sz;
Node *l, *r;
line e;
int L;
Node(line _e, int _L) {
y = rng();
sz = 1;
l = r = 0;
e = _e;
L = _L;
}
};
int sz(Node* t) {
return t ? t->sz : 0;
}
void upd(Node* t) {
if (t) {
t->sz = sz(t->l) + 1 + sz(t->r);
}
}
Node* merge(Node* a, Node* b) {
if (!a) return b;
if (!b) return a;
if (a->y > b->y) {
a->r = merge(a->r, b);
upd(a);
return a;
} else {
b->l = merge(a, b->l);
upd(b);
return b;
}
}
void travel(Node* t, function<void(line, int)> f) {
if (!t) return;
travel(t->l, f);
f(t->e, t->L);
travel(t->r, f);
}
void clear(Node *t) {
if (!t) return;
clear(t->l);
clear(t->r);
//delete t;
}
pair<line, int> getLeft(Node *t) {
assert(t);
while (t->l)
t = t->l;
return {t->e, t->L};
}
void removeLeft(Node*& t) {
if (!t) return;
if (t->l) {
removeLeft(t->l);
upd(t);
} else {
auto tt = merge(t->l, t->r);
// delete t;
t = tt;
}
}
void addToAll(Node* t, ll delta) {
if (!t) return;
addToAll(t->l, delta);
t->e.b += delta;
addToAll(t->r, delta);
}
ll f(Node *t, int i) {
ll ans = 0;
while (t) {
if (t->L <= i) {
ans = t->e.f(i);
t = t->r;
} else {
t = t->l;
}
}
return ans;
}
}
struct DS {
ll delta;
treap::Node* T;
int R;
DS() {
delta = 0;
T = 0;
}
DS(ll x, int l) {
delta = 0;
/*val = {{0, x}};
L = {l};*/
T = new treap::Node({0, x}, l);
}
void clear() {
delta = 0;
treap::clear(T);
T = 0;
}
int size() {
return treap::sz(T);
}
void pushBack(line e, int l) {
e.b -= delta;
T = treap::merge(T, new treap::Node(e, l));
}
void pushFront(line e, int l) {
e.b -= delta;
T = treap::merge(new treap::Node(e, l), T);
}
void pushBack(int i, ll x) {
x -= delta;
T = treap::merge(T, new treap::Node({0, x}, i));
}
void pushFront(int i, ll x) {
x -= delta;
T = treap::merge(new treap::Node({0, x}, i), T);
}
void add(ll d) {
delta += d;
}
void relaxPrefix(line e) {
/*if (val.empty()) return;
e.b -= delta;
if (val[0].f(L[0]) <= e.f(L[0])) return;
int l = L[0];
while (!val.empty() && val[0].f(L[0]) > e.f(L[0])) {
int r = (val.size() > 1 ? L[1] - 1 : R);
if (val[0].f(r) >= e.f(r)) {
val.pop_front();
L.pop_front();
} else {
L[0] = ceil(intersect(e, val[0]));
break;
}
}
val.push_front(e);
L.push_front(l);*/
if (!T) return;
e.b -= delta;
line e1;
int L1;
tie(e1, L1) = treap::getLeft(T);
int l = L1;
if (e1.f(L1) <= e.f(L1)) return;
while (T && e1.f(L1) > e.f(L1)) {
treap::removeLeft(T);
int r = T ? treap::getLeft(T).se - 1 : R;
if (e1.f(r) >= e.f(r)) {
if (!T) break;
tie(e1, L1) = treap::getLeft(T);
} else {
T = treap::merge(new treap::Node(e1, ceil(intersect(e, e1))), T);
break;
}
}
T = treap::merge(new treap::Node(e, l), T);
}
ll f(int i) {
// int t = upper_bound(all(L), i) - L.begin() - 1;
// if (t < 0) return 0;
// return val[t].f(i) + delta;
return treap::f(T, i) + delta;
}
};// PP[maxN];
vector<ll> minimum_costs(vector<int> _a, vector<int> ql, vector<int> qr) {
n = _a.size(), Q = ql.size();
for (int i = 0; i < n; ++i)
a[i] = _a[i];
iota(randY, randY + n, 0);
shuffle(randY, randY + n, rng);
for (int i = 0; i < n; ++i)
irandY[randY[i]] = i;
vector<ll> ans(Q, INF64);
for (int rot = 0; rot < 2; ++rot) {
for (int i = 0; i < n; ++i) {
que[i].clear();
// PP[i].clear();
}
sgt::build(rot);
for (int i = 0; i < Q; ++i) {
int j = sgt::argmax(ql[i], qr[i]);
que[j].push_back(i);
}
function<DS(int, int)> solve = [&](int L, int R) {
if (L > R) return DS();
int I = sgt::argmax(L, R);
ll M = a[I];
// debug(L, I, R);
// auto& P = PP[I];
// int IL = solve(L, I - 1);
// auto& PL = PP[IL];
// int IR = solve(I + 1, R);
// auto& PR = PP[IR];
DS P;
P.R = R;
DS PL = solve(L, I - 1);
DS PR = solve(I + 1, R);
for (int q : que[I]) {
int l = ql[q], r = qr[q];
chkmin(ans[q], PR.f(r) + M * (I - l + 1));
}
PR.add(M * (I - L + 1));
PR.relaxPrefix({M, PL.f(I - 1) - M * (I - 1)});
if (PR.size() <= PL.size()) {
swap(P, PL);
P.R = R;
P.pushBack(I, P.f(I - 1) + M);
// for (int i = 0; i < PR.size(); ++i) {
// line e = PR.val[i];
// e.b += PR.delta;
// int l = PR.L[i];
// P.pushBack(e, l);
// }
// for (int i = I + 1, t = 0; i <= R; ++i) {
// while (t + 1 < PR.size() && PR.L[t + 1] <= i)
// ++t;
// P.pushBack(i, PR.val[t].f(i) + PR.delta);
// }
treap::addToAll(PR.T, + PR.delta - P.delta);
P.T = treap::merge(P.T, PR.T);
PR.clear();
} else {
swap(P, PR);
P.R = R;
P.pushFront(I, PL.f(I - 1) + M);
// for (int i = (int)PL.size() - 1; i >= 0; --i) {
// line e = PL.val[i];
// e.b += PL.delta;
// int l = PL.L[i];
// P.pushFront(e, l);
// }
// for (int i = I - 1, t = PL.size() - 1; i >= L; --i) {
// while (PL.L[t] > i)
// --t;
// P.pushFront(i, PL.val[t].f(i) + PL.delta);
// }
treap::addToAll(PL.T, + PL.delta - P.delta);
P.T = treap::merge(PL.T, P.T);
PL.clear();
}
// debug(L, I, R);
// for (int i = L; i <= R; ++i)
// cerr << P.f(i) << ' ';
// cerr << endl;
// debug(ans);
return P;
// return I;
};
auto P = solve(0, n - 1);
P.clear();
reverse(a, a + n);
reverse(randY, randY + n);
for (int i = 0; i < n; ++i)
irandY[randY[i]] = i;
for (int i = 0; i < Q; ++i) {
ql[i] = n - ql[i] - 1;
qr[i] = n - qr[i] - 1;
swap(ql[i], qr[i]);
}
}
return ans;
}
#ifdef LOCAL
int read_int() {
int x;
if (scanf("%d", &x) != 1) {
fprintf(stderr, "Error while reading input\n");
exit(1);
}
return x;
}
int32_t main() {
#ifdef LOCAL
freopen("in", "r", stdin);
#endif
ios::sync_with_stdio(0);
cin.tie(0);
int N = read_int();
int Q = read_int();
std::vector<int> H(N);
for (int i = 0; i < N; ++i) {
H[i] = read_int();
}
std::vector<int> L(Q), R(Q);
for (int j = 0; j < Q; ++j) {
L[j] = read_int();
R[j] = read_int();
}
std::vector<long long> C = minimum_costs(H, L, R);
for (size_t j = 0; j < C.size(); ++j) {
printf("%lld\n", C[j]);
}
return 0;
return 0;
}
#endif
