#include <bits/stdc++.h>
#ifndef LOCAL
#include "meetings.h"
#endif //nLOCAL
using namespace std;
#define FOR(i, l, r) for(int i = (l); i < (r); ++i)
#define ROF(i, r, l) for(int i = (r) - 1; i >= (l); --i)
#define mp make_pair
#define mt make_tuple
#define ff first
#define ss second
#define all(v) begin(v), end(v)
#define rall(v) rbegin(v), rend(v)
#define pb push_back
#define eb emplace_back
#define sz(v) (int)v.size()
#define sum_of(v) accumulate(all(v), 0ll)
#define compact(v) v.erase(unique(all(v)), end(v))
#define dbg(x) "[" #x " = " << (x) << "]"
template<typename T>
bool minimize(T& a, const T& b){
if(a > b) return a = b, true;
return false;
}
template<typename T>
bool maximize(T& a, const T& b){
if(a < b) return a = b, true;
return false;
}
using ll = long long;
using db = double;
using ld = long double;
using ull = unsigned long long;
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<db, db>;
using vi = vector<int>;
using vb = vector<bool>;
using vc = vector<char>;
using vl = vector<ll>;
using vd = vector<db>;
using vpi = vector<pi>;
using vpl = vector<pl>;
/*
Extended Li-chao Tree features :
- 1 l r a b : for all i in [l, r] : v[i] = min(v[i], a * i + b)
- 2 l r a b : for all i in [l, r] : v[i] += a * i + b
- 3 p : return a[p]
*/
struct line{
ll a, b;
line(ll a, ll b) : a(a), b(b) {}
ll operator()(ll x) const { return a * x + b; }
ll slope(){ return a; }
ll intercept(){ return b; }
line& operator += (const line& o){
a += o.a; b += o.b;
return *this;
}
friend line operator + (line a, const line& b){ return a += b; }
};
const ll inf = 1e17;
struct MinExtendedLichaoTree{
vector<line> st, lazy;
MinExtendedLichaoTree(int n) : st(n << 2, line(0, 0)), lazy(n << 2, line(0, 0)) {}
void apply_increase(int id, line f){
if(st[id].a != 0 || st[id].b != inf) {
st[id] += f;
}
lazy[id] += f;
}
void push_down(int id){
if(lazy[id].a != 0 || lazy[id].b != 0){
apply_increase(id << 1, lazy[id]);
apply_increase(id << 1 | 1, lazy[id]);
lazy[id].a = lazy[id].b = 0;
}
}
void add_line(int id, int l, int r, line f){
if(l == r){
if(st[id](l) > f(l)) st[id] = f;
} else{
int mid = l + r >> 1;
push_down(id);
if(st[id](mid) > f(mid)) swap(st[id], f);
if(f.a > st[id].a) add_line(id << 1, l, mid, f);
if(f.a < st[id].a) add_line(id << 1 | 1, mid + 1, r, f);
}
}
void push_line(int id, int l, int r, int mid){
if(st[id].b != inf){
add_line(id << 1, l, mid, st[id]);
add_line(id << 1 | 1, mid + 1, r, st[id]);
st[id].a = 0;
st[id].b = inf;
}
}
void update_add_line(int id, int l, int r, int u, int v, line f){
if(u <= l && r <= v){
add_line(id, l, r, f);
} else{
int mid = l + r >> 1;
push_down(id);
if(u <= mid) update_add_line(id << 1, l, mid, u, v, f);
if(mid < v) update_add_line(id << 1 | 1, mid + 1, r, u, v, f);
}
}
void update_increase(int id, int l, int r, int u, int v, line f){
if(u <= l && r <= v) {
apply_increase(id, f);
}
else{
int mid = l + r >> 1;
push_down(id);
push_line(id, l, r, mid);
if(u <= mid) update_increase(id << 1, l, mid, u, v, f);
if(mid < v) update_increase(id << 1 | 1, mid + 1, r, u, v, f);
}
}
ll query_point(int id, int l, int r, int pos){
ll cur = st[id](pos);
if(l == r) return cur;
int mid = l + r >> 1;
push_down(id);
if(pos <= mid) return min(cur, query_point(id << 1, l, mid, pos));
else return min(cur, query_point(id << 1 | 1, mid + 1, r, pos));
}
};
template<typename T>
struct MaxSparseTable{
vector<vector<T>> rmq;
MaxSparseTable(vector<T> v) : rmq(){
rmq.pb(v);
int N = sz(v);
for(int i = 1; (1 << i) <= N; ++i){
rmq.pb(vector<T>(N - (1 << i) + 1));
FOR(j, 0, N - (1 << i) + 1){
rmq[i][j] = max(rmq[i-1][j], rmq[i-1][j + (1 << (i-1))]);
}
}
}
T query(int l, int r){
int k = 31 - __builtin_clz(r - l + 1);
return max(rmq[k][l], rmq[k][r - (1 << k) + 1]);
}
};
vl minimum_costs(vi H, vi L, vi R){
int N = sz(H);
int Q = sz(L);
vpi v(N);
FOR(i, 0, N){
v[i] = mp(H[i], i);
}
MaxSparseTable<pi> ST(v);
vector<vi> pos(N);
FOR(i, 0, Q){
int p = ST.query(L[i], R[i]).ss;
pos[p].pb(i);
}
MinExtendedLichaoTree le(N), re(N);
vl ans(Q, -1);
function<void(int, int)> solve = [&](int l, int r){
int M = ST.query(l, r).ss;
if(l < M) solve(l, M-1);
if(M < r) solve(M+1, r);
//le : opt[L][M-1], opt[L+1][M-1], ..., opt[M-1][M-1] ; opt[M+1][R], opt[M+2][R], ..., opt[R][R]
//re : opt[L][L], opt[L][L+1], ..., opt[L][M-1] ; opt[M+1][M+1], opt[M+1][M+2], ..., opt[M+1][R] ;
for(auto id : pos[M]){
ans[id] = min(le.query_point(1, 0, N-1, L[id]) + 1LL * (R[id] - M + 1) * H[M],
re.query_point(1, 0, N-1, R[id]) + 1LL * (M - L[id] + 1) * H[M]);
}
//opt[x][R] = min(opt[x][M-1] + (R - M + 1) * H[M], opt[M+1][R] + M * H[M] + H[M] - x * H[M])
//opt[L][x] = min(opt[L][M-1] + x * H[M] - M * H[M] + H[M], opt[M+1][x] + (M - L + 1) * H[M])
ll optRight = (M<r ? le.query_point(1, 0, N-1, M+1) : 0);
le.update_increase(1, 0, N-1, l, M, line(0, 1LL * (r - M + 1) * H[M]));
le.update_add_line(1, 0, N-1, l, M, line(-H[M], 1LL * M * H[M] + H[M] + optRight));
ll optLeft = (l<M ? re.query_point(1, 0, N-1, M-1) : 0);
re.update_increase(1, 0, N-1, M, r, line(0, 1LL * (M - l + 1) * H[M]));
re.update_add_line(1, 0, N-1, M, r, line(H[M], -1LL * M * H[M] + H[M] + optLeft));
};
solve(0, N-1);
return ans;
}
#ifdef LOCAL
void setIO(){
ios_base::sync_with_stdio(0); cin.tie(0);
#ifdef LOCAL
freopen("task.inp", "r", stdin);
freopen("task.out", "w", stdout);
#endif // LOCAL
}
int main(){
setIO();
int N, Q;
cin >> N >> Q;
vi H(N);
FOR(i, 0, N) cin >> H[i];
vi L(Q), R(Q);
FOR(i, 0, Q){
cin >> L[i] >> R[i];
}
vl result = minimum_costs(H, L, R);
FOR(i, 0, Q) cout << result[i] << '\n';
return 0;
}
#endif //LOCAL
/*
Let f[L][R] = the answer for query [L, R]
Consider query [L, R] :
- Let (H[p], p) become the maximum (H[i], i) for L <= i <= R
- f[L][R] = min(f[L][p-1] + (R - p + 1) * H[p], f[p+1][R] + (p - L + 1) * H[p])
Let recursively solve f[L][p-1] and f[p+1][R]
Assume that we had calculated f[1][p-1], f[L][p-1], ..., f[p-1][p-1] :
- for every p < R : f[L][R] = f[L][p-1] + (R - p + 1) * H[p]
- then f[L][R] = min(f[L][R], f[p+1][R] + (p - L + 1) * H[p])
*/
