Static Range Inversions Query

#include <algorithm>
#include <iostream>
#include <vector>
 
using namespace std;
using ll = long long;
using P = pair<int, int>;
const int N = 1e5 + 1;
const int S = 300;
 
// BeginCodeSnip{BIT (from PURS module)}
template <class T> class BIT {
  private:
	int size;
	vector<T> bit;
	vector<T> arr;
 
  public:
	BIT(int size) : size(size), bit(size + 1), arr(size) {}
 
	/** Sets the value at index ind to val. */
	void set(int ind, T val) { add(ind, val - arr[ind]); }
 
	/** Adds val to the element at index ind. */
	void add(int ind, T val) {
		arr[ind] += val;
		ind++;
		for (; ind <= size; ind += ind & -ind) { bit[ind] += val; }
	}
 
	/** @return The sum of all values in [0, ind]. */
	T pref_sum(int ind) {
		ind++;
		T total = 0;
		for (; ind > 0; ind -= ind & -ind) { total += bit[ind]; }
		return total;
	}
};
// EndCodeSnip
 
struct Query {
	int l, r, i;
};
 
int main() {
	int n, k;
	cin >> n >> k;
	vector<int> a(n);
	for (int i = 0; i < n; i++) { cin >> a[i]; }
	vector<int> b(a);
	sort(b.begin(), b.end());
	b.erase(unique(b.begin(), b.end()), b.end());
 
	auto id = [&](int x) { return lower_bound(b.begin(), b.end(), a[x]) - b.begin(); };
 
	vector<Query> q(k);
	for (int i = 0; i < k; i++) {
		q[i].i = i;
		cin >> q[i].l >> q[i].r;
	}
	q.push_back({0, 0, -1});  // add dummy initial query
	sort(q.begin(), q.end(), [](Query x, Query y) {
		if (x.l / S != y.l / S) return x.l / S < y.l / S;
		else return x.r < y.r;
	});
 
	ll res = 0;
	BIT<int> bit(n);
	// left -> whether we're modifying on the left
	auto edit = [&](int id, int x, bool left) {
		res +=
		    (left ? bit.pref_sum(id - 1) : bit.pref_sum(n - 1) - bit.pref_sum(id)) * x;
		bit.add(id, x);
	};
 
	vector<ll> ans(k);
	for (int i = 0; i < q.size(); i++) {
		if (i) { ans[q[i].i] = res; }
		if (i + 1 >= q.size()) { break; }
		while (q[i].l > q[i + 1].l) { edit(id(--q[i].l), 1, true); }
		while (q[i].r < q[i + 1].r) { edit(id(q[i].r++), 1, false); }
		while (q[i].l < q[i + 1].l) { edit(id(q[i].l++), -1, true); }
		while (q[i].r > q[i + 1].r) { edit(id(--q[i].r), -1, false); }
	}
 
	for (int i = 0; i < k; i++) { cout << ans[i] << '\n'; }
}

#include <bits/stdc++.h>
using namespace std;
 
using ll = long long;
using ld = long double;
using db = double;
using str = string;  // yay python!
 
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<db, db>;
 
using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vd = vector<db>;
using vs = vector<str>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vpd = vector<pd>;
 
#define tcT template <class T
#define tcTU tcT, class U
// ^ lol this makes everything look weird but I'll try it
tcT > using V = vector<T>;
tcT, size_t SZ > using AR = array<T, SZ>;
tcT > using PR = pair<T, T>;
 
// pairs
#define mp make_pair
#define f first
#define s second
 
// vectors
// oops size(x), rbegin(x), rend(x) need C++17
#define sz(x) int((x).size())
#define bg(x) begin(x)
#define all(x) bg(x), end(x)
#define rall(x) x.rbegin(), x.rend()
#define sor(x) sort(all(x))
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
#define pb push_back
#define eb emplace_back
#define pf push_front
 
#define lb lower_bound
#define ub upper_bound
tcT > int lwb(V<T> &a, const T &b) { return int(lb(all(a), b) - bg(a)); }
 
// loops
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define F0R(i, a) FOR(i, 0, a)
#define ROF(i, a, b) for (int i = (b) - 1; i >= (a); --i)
#define R0F(i, a) ROF(i, 0, a)
#define trav(a, x) for (auto &a : x)
 
const int MOD = 1e9 + 7;  // 998244353;
const int MX = 2e5 + 5;
const ll INF = 1e18;  // not too close to LLONG_MAX
const ld PI = acos((ld)-1);
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};  // for every grid problem!!
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
 
// bitwise ops
// also see https://gcc.gnu.org/onlinedocs/gcc/Other-Builtins.html
constexpr int pct(int x) { return __builtin_popcount(x); }  // # of bits set
constexpr int bits(int x) {  // assert(x >= 0); // make C++11 compatible until
	                         // USACO updates ...
	return x == 0 ? 0 : 31 - __builtin_clz(x);
}  // floor(log2(x))
constexpr int p2(int x) { return 1 << x; }
constexpr int msk2(int x) { return p2(x) - 1; }
 
ll cdiv(ll a, ll b) {
	return a / b + ((a ^ b) > 0 && a % b);
}  // divide a by b rounded up
ll fdiv(ll a, ll b) {
	return a / b - ((a ^ b) < 0 && a % b);
}  // divide a by b rounded down
 
tcT > bool ckmin(T &a, const T &b) { return b < a ? a = b, 1 : 0; }  // set a = min(a,b)
tcT > bool ckmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; }
 
tcTU > T fstTrue(T lo, T hi, U f) {
	hi++;
	assert(lo <= hi);  // assuming f is increasing
	while (lo < hi) {  // find first index such that f is true
		T mid = lo + (hi - lo) / 2;
		f(mid) ? hi = mid : lo = mid + 1;
	}
	return lo;
}
tcTU > T lstTrue(T lo, T hi, U f) {
	lo--;
	assert(lo <= hi);  // assuming f is decreasing
	while (lo < hi) {  // find first index such that f is true
		T mid = lo + (hi - lo + 1) / 2;
		f(mid) ? lo = mid : hi = mid - 1;
	}
	return lo;
}
tcT > void remDup(vector<T> &v) {  // sort and remove duplicates
	sort(all(v));
	v.erase(unique(all(v)), end(v));
}
tcTU > void erase(T &t, const U &u) {  // don't erase
	auto it = t.find(u);
	assert(it != end(t));
	t.erase(it);
}  // element that doesn't exist from (multi)set
 
// INPUT
#define tcTUU tcT, class... U
tcT > void re(complex<T> &c);
tcTU > void re(pair<T, U> &p);
tcT > void re(V<T> &v);
tcT, size_t SZ > void re(AR<T, SZ> &a);
 
tcT > void re(T &x) { cin >> x; }
void re(db &d) {
	str t;
	re(t);
	d = stod(t);
}
void re(ld &d) {
	str t;
	re(t);
	d = stold(t);
}
tcTUU > void re(T &t, U &...u) {
	re(t);
	re(u...);
}
 
tcT > void re(complex<T> &c) {
	T a, b;
	re(a, b);
	c = {a, b};
}
tcTU > void re(pair<T, U> &p) { re(p.f, p.s); }
tcT > void re(V<T> &x) { trav(a, x) re(a); }
tcT, size_t SZ > void re(AR<T, SZ> &x) { trav(a, x) re(a); }
tcT > void rv(int n, V<T> &x) {
	x.rsz(n);
	re(x);
}
 
// TO_STRING
#define ts to_string
str ts(char c) { return str(1, c); }
str ts(const char *s) { return (str)s; }
str ts(str s) { return s; }
str ts(bool b) {
#ifdef LOCAL
	return b ? "true" : "false";
#else
	return ts((int)b);
#endif
}
tcT > str ts(complex<T> c) {
	stringstream ss;
	ss << c;
	return ss.str();
}
str ts(V<bool> v) {
	str res = "{";
	F0R(i, sz(v)) res += char('0' + v[i]);
	res += "}";
	return res;
}
template <size_t SZ> str ts(bitset<SZ> b) {
	str res = "";
	F0R(i, SZ) res += char('0' + b[i]);
	return res;
}
tcTU > str ts(pair<T, U> p);
tcT > str ts(T v) {  // containers with begin(), end()
#ifdef LOCAL
	bool fst = 1;
	str res = "{";
	for (const auto &x : v) {
		if (!fst) res += ", ";
		fst = 0;
		res += ts(x);
	}
	res += "}";
	return res;
#else
	bool fst = 1;
	str res = "";
	for (const auto &x : v) {
		if (!fst) res += " ";
		fst = 0;
		res += ts(x);
	}
	return res;
 
#endif
}
tcTU > str ts(pair<T, U> p) {
#ifdef LOCAL
	return "(" + ts(p.f) + ", " + ts(p.s) + ")";
#else
	return ts(p.f) + " " + ts(p.s);
#endif
}
 
// OUTPUT
tcT > void pr(T x) { cout << ts(x); }
tcTUU > void pr(const T &t, const U &...u) {
	pr(t);
	pr(u...);
}
void ps() { pr("\n"); }  // print w/ spaces
tcTUU > void ps(const T &t, const U &...u) {
	pr(t);
	if (sizeof...(u)) pr(" ");
	ps(u...);
}
 
// DEBUG
void DBG() { cerr << "]" << endl; }
tcTUU > void DBG(const T &t, const U &...u) {
	cerr << ts(t);
	if (sizeof...(u)) cerr << ", ";
	DBG(u...);
}
#ifdef LOCAL  // compile with -DLOCAL, chk -> fake assert
#define dbg(...)                                                                       \
	cerr << "Line(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#define chk(...)                                                                       \
	if (!(__VA_ARGS__))                                                                \
		cerr << "Line(" << __LINE__ << ") -> function(" << __FUNCTION__                \
		     << ") -> CHK FAILED: (" << #__VA_ARGS__ << ")" << "\n",                   \
		    exit(0);
#else
#define dbg(...) 0
#define chk(...) 0
#endif
 
void setPrec() { cout << fixed << setprecision(15); }
void unsyncIO() { cin.tie(0)->sync_with_stdio(0); }
// FILE I/O
void setIn(str s) { freopen(s.c_str(), "r", stdin); }
void setOut(str s) { freopen(s.c_str(), "w", stdout); }
void setIO(str s = "") {
	unsyncIO();
	setPrec();
	// cin.exceptions(cin.failbit);
	// throws exception when do smth illegal
	// ex. try to read letter into int
	if (sz(s)) setIn(s + ".in"), setOut(s + ".out");  // for USACO
}
 
const int BLOCK = 320;
int N, Q;
vi A;
V<AR<int, 3>> query;
 
void init() {
	setIO();
	re(N, Q);
	A.rsz(N);
	re(A);
	vi al;
	trav(t, A) al.pb(t);
	remDup(al);
	trav(t, A) t = int(lb(all(al), t) - begin(al));
	F0R(i, Q) {
		int l, r;
		re(l, r);
		r--;
		query.pb({l, r, i});
	}
}
 
V<AR<int, 4>> adLes[100000], adGre[100000];
int les[BLOCK * BLOCK], les_block[BLOCK], tot;
int numLes(int x) { return les[x] + les_block[x / BLOCK]; }
void insLes(int x) {
	++tot;
	for (++x; x % BLOCK;) les[x++]++;
	for (x /= BLOCK; x < BLOCK;) les_block[x++]++;
}
int numGre(int x) { return tot - numLes(x + 1); }
 
vl dif;
vi prevLes, prevGre;
 
void preprocess_queries() {
	sort(all(query), [](AR<int, 3> a, AR<int, 3> b) {
		return a[0] / BLOCK == b[0] / BLOCK ? a[1] < b[1] : a[0] < b[0];
	});
	prevLes.rsz(N), prevGre.rsz(N);
	dif.rsz(Q);
	int l = 0, r = 0;
	trav(t, query) {
		if (l > t[0]) {  // add how many < x in range [cur,r]
			adLes[r].pb({t[0], l - 1, 1, t[2]});
			l = t[0];
		}
		if (r < t[1]) {  // add how many > x in range[l,cur]
			if (l) adGre[l - 1].pb({r + 1, t[1], -1, t[2]});
			r = t[1];  // (0,0) -> (0,1) -> (0,2)
		}
		if (l < t[0]) {  // subtract how many < x in range[cur,r]
			adLes[r].pb({l, t[0] - 1, -1, t[2]});
			l = t[0];
		}
		if (r > t[1]) {  // subtract how many > x in range[l,cur]
			if (l) adGre[l - 1].pb({t[1] + 1, r, 1, t[2]});
			r = t[1];
		}
	}
	F0R(i, N) {
		insLes(A[i]);
		prevLes[i] = numLes(A[i]), prevGre[i] = numGre(A[i]);
		trav(t, adLes[i]) {
			ll sum = 0;
			FOR(j, t[0], t[1] + 1) sum += numLes(A[j]);
			dif[t[3]] += t[2] * sum;
		}
		trav(t, adGre[i]) {
			ll sum = 0;
			FOR(j, t[0], t[1] + 1) sum += numGre(A[j]);
			dif[t[3]] += t[2] * sum;
		}
	}
}
 
int main() {
	init();
	preprocess_queries();
	ll lastAns = 0;
	vl ans(Q);
	int l = 0, r = 0;
	trav(t, query) {
		while (l > t[0]) dif[t[2]] -= prevLes[--l];
		while (r < t[1]) dif[t[2]] += prevGre[++r];
		while (l < t[0]) dif[t[2]] += prevLes[l++];
		while (r > t[1]) dif[t[2]] -= prevGre[r--];
		ans[t[2]] = (lastAns += dif[t[2]]);
	}
	trav(t, ans) ps(t);
}