#line 1 "/home/maspy/compro/library/my_template.hpp"
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using pi = pair<ll, ll>;
using vi = vector<ll>;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;

template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#define vec(type, name, ...) vector<type> name(__VA_ARGS__)
#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define FOR4_R(i, a, b, c) for (ll i = (b)-1; i >= ll(a); i -= (c))
#define overload4(a, b, c, d, e, ...) e
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) \
  overload4(__VA_ARGS__, FOR4_R, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define FOR_subset(t, s) for (ll t = s; t >= 0; t = (t == 0 ? -1 : (t - 1) & s))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sum = 0;
  for (auto &&a: A) sum += a;
  return sum;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end())

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
T pick(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}

template <typename T>
T pick(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}

template <typename T>
T pick(pqg<T> &que) {
  assert(que.size());
  T a = que.top();
  que.pop();
  return a;
}

template <typename T>
T pick(vc<T> &que) {
  assert(que.size());
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename T, typename U>
T ceil(T x, U y) {
  return (x > 0 ? (x + y - 1) / y : x / y);
}

template <typename T, typename U>
T floor(T x, U y) {
  return (x > 0 ? x / y : (x - y + 1) / y);
}

template <typename T, typename U>
pair<T, T> divmod(T x, U y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename F>
ll binary_search(F check, ll ok, ll ng) {
  assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x));
  }
  return ok;
}

template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x));
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = S[i] - first_char; }
  return A;
}

template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

template <typename CNT, typename T>
vc<CNT> bincount(const vc<T> &A, int size) {
  vc<CNT> C(size);
  for (auto &&x: A) { ++C[x]; }
  return C;
}

// stable
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(A.size());
  iota(all(ids), 0);
  sort(all(ids),
       [&](int i, int j) { return A[i] < A[j] || (A[i] == A[j] && i < j); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  int n = len(I);
  vc<T> B(n);
  FOR(i, n) B[i] = A[I[i]];
  return B;
}
#line 1 "/home/maspy/compro/library/other/io.hpp"
// based on yosupo's fastio
#include <unistd.h>

namespace detail {
template <typename T, decltype(&T::is_modint) = &T::is_modint>
std::true_type check_value(int);
template <typename T>
std::false_type check_value(long);
} // namespace detail

template <typename T>
struct is_modint : decltype(detail::check_value<T>(0)) {};
template <typename T>
using is_modint_t = enable_if_t<is_modint<T>::value>;
template <typename T>
using is_not_modint_t = enable_if_t<!is_modint<T>::value>;

struct Scanner {
  FILE *fp;
  char line[(1 << 15) + 1];
  size_t st = 0, ed = 0;
  void reread() {
    memmove(line, line + st, ed - st);
    ed -= st;
    st = 0;
    ed += fread(line + ed, 1, (1 << 15) - ed, fp);
    line[ed] = '\0';
  }
  bool succ() {
    while (true) {
      if (st == ed) {
        reread();
        if (st == ed) return false;
      }
      while (st != ed && isspace(line[st])) st++;
      if (st != ed) break;
    }
    if (ed - st <= 50) {
      bool sep = false;
      for (size_t i = st; i < ed; i++) {
        if (isspace(line[i])) {
          sep = true;
          break;
        }
      }
      if (!sep) reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    while (true) {
      size_t sz = 0;
      while (st + sz < ed && !isspace(line[st + sz])) sz++;
      ref.append(line + st, sz);
      st += sz;
      if (!sz || st != ed) break;
      reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    bool neg = false;
    if (line[st] == '-') {
      neg = true;
      st++;
    }
    ref = T(0);
    while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); }
    if (neg) ref = -ref;
    return true;
  }
  template <class T, is_modint_t<T> * = nullptr>
  bool read_single(T &ref) {
    long long val = 0;
    bool f = read_single(val);
    ref = T(val);
    return f;
  }
  bool read_single(double &ref) {
    string s;
    if (!read_single(s)) return false;
    ref = std::stod(s);
    return true;
  }
  bool read_single(char &ref) {
    string s;
    if (!read_single(s) || s.size() != 1) return false;
    ref = s[0];
    return true;
  }
  template <class T>
  bool read_single(vector<T> &ref) {
    for (auto &d: ref) {
      if (!read_single(d)) return false;
    }
    return true;
  }
  template <class T, class U>
  bool read_single(pair<T, U> &p) {
    return (read_single(p.first) && read_single(p.second));
  }
  template <class A, class B, class C>
  bool read_single(tuple<A, B, C> &p) {
    return (read_single(get<0>(p)) && read_single(get<1>(p))
            && read_single(get<2>(p)));
  }
  template <class A, class B, class C, class D>
  bool read_single(tuple<A, B, C, D> &p) {
    return (read_single(get<0>(p)) && read_single(get<1>(p))
            && read_single(get<2>(p)) && read_single(get<3>(p)));
  }
  void read() {}
  template <class H, class... T>
  void read(H &h, T &... t) {
    bool f = read_single(h);
    assert(f);
    read(t...);
  }
  Scanner(FILE *fp) : fp(fp) {}
};

struct Printer {
  Printer(FILE *_fp) : fp(_fp) {}
  ~Printer() { flush(); }

  static constexpr size_t SIZE = 1 << 15;
  FILE *fp;
  char line[SIZE], small[50];
  size_t pos = 0;
  void flush() {
    fwrite(line, 1, pos, fp);
    pos = 0;
  }
  void write(const char &val) {
    if (pos == SIZE) flush();
    line[pos++] = val;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  void write(T val) {
    if (pos > (1 << 15) - 50) flush();
    if (val == 0) {
      write('0');
      return;
    }
    if (val < 0) {
      write('-');
      val = -val; // todo min
    }
    size_t len = 0;
    while (val) {
      small[len++] = char(0x30 | (val % 10));
      val /= 10;
    }
    for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; }
    pos += len;
  }
  void write(const string &s) {
    for (char c: s) write(c);
  }
  void write(const char *s) {
    size_t len = strlen(s);
    for (size_t i = 0; i < len; i++) write(s[i]);
  }
  void write(const double &x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  void write(const long double &x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  template <class T, is_modint_t<T> * = nullptr>
  void write(T &ref) {
    write(ref.val);
  }
  template <class T>
  void write(const vector<T> &val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  template <class T, class U>
  void write(const pair<T, U> &val) {
    write(val.first);
    write(' ');
    write(val.second);
  }
  template <class A, class B, class C>
  void write(const tuple<A, B, C> &val) {
    auto &[a, b, c] = val;
    write(a), write(' '), write(b), write(' '), write(c);
  }
  template <class A, class B, class C, class D>
  void write(const tuple<A, B, C, D> &val) {
    auto &[a, b, c, d] = val;
    write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d);
  }
  template <class A, class B, class C, class D, class E>
  void write(const tuple<A, B, C, D, E> &val) {
    auto &[a, b, c, d, e] = val;
    write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e);
  }
  template <class A, class B, class C, class D, class E, class F>
  void write(const tuple<A, B, C, D, E, F> &val) {
    auto &[a, b, c, d, e, f] = val;
    write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e), write(' '), write(f);
  }
  template <class T, size_t S>
  void write(const array<T, S> &val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  void write(i128 val) {
    string s;
    bool negative = 0;
    if(val < 0){
      negative = 1;
      val = -val;
    }
    while (val) {
      s += '0' + int(val % 10);
      val /= 10;
    }
    if(negative) s += "-";
    reverse(all(s));
    if (len(s) == 0) s = "0";
    write(s);
  }
};

Scanner scanner = Scanner(stdin);
Printer printer = Printer(stdout);

void flush() { printer.flush(); }
void print() { printer.write('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  printer.write(head);
  if (sizeof...(Tail)) printer.write(' ');
  print(forward<Tail>(tail)...);
}

void read() {}
template <class Head, class... Tail>
void read(Head &head, Tail &... tail) {
  scanner.read(head);
  read(tail...);
}

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define CHAR(...)      \
  char __VA_ARGS__; \
  read(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  read(__VA_ARGS__)

#define VEC(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  read(name)

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 2 "/home/maspy/compro/library/alg/group_add.hpp"

template <typename E>
struct Group_Add {
  using X = E;
  using value_type = X;
  static constexpr X op(const X &x, const X &y) noexcept { return x + y; }
  static constexpr X inverse(const X &x) noexcept { return -x; }
  static constexpr X power(const X &x, ll n) noexcept { return X(n) * x; }
  static constexpr X unit() { return X(0); }
  static constexpr bool commute = true;
};
#line 3 "/home/maspy/compro/library/ds/fenwick.hpp"

template <typename AbelGroup>
struct FenwickTree {
  using E = typename AbelGroup::value_type;
  int n;
  vector<E> dat;
  E total;

  FenwickTree(int n = 0) : n(n) {
    assert(AbelGroup::commute);
    reset(n);
  }
  FenwickTree(const vector<E>& v) {
    assert(AbelGroup::commute);
    build(v);
  }

  void build(const vc<E>& v) {
    n = len(v);
    total = AbelGroup::unit();
    for (int i = 0; i < n; ++i) total = AbelGroup::op(total, v[i]);
    dat = v;
    for (int i = 1; i <= n; ++i) {
      int j = i + (i & -i);
      if (j <= n) dat[j - 1] = AbelGroup::op(dat[i - 1], dat[j - 1]);
    }
  }

  void reset(int sz = 0) {
    if (sz) n = sz;
    total = AbelGroup::unit();
    dat.assign(n, AbelGroup::unit());
  }

  E prod(int k) {
    E ret = AbelGroup::unit();
    for (; k > 0; k -= k & -k) ret = AbelGroup::op(ret, dat[k - 1]);
    return ret;
  }

  E prod(int L, int R) {
    E pos = AbelGroup::unit();
    while (L < R) {
      pos = AbelGroup::op(pos, dat[R - 1]);
      R -= R & -R;
    }
    E neg = AbelGroup::unit();
    while (R < L) {
      neg = AbelGroup::op(neg, dat[L - 1]);
      L -= L & -L;
    }
    return AbelGroup::op(pos, AbelGroup::inverse(neg));
  }

  E prod_all() { return total; }

  E sum(int k) { return prod(k); }

  E sum(int L, int R) { return prod(L, R); }

  E sum_all() { return total; }

  void multiply(int k, E x) {
    total = AbelGroup::op(total, x);
    for (++k; k <= n; k += k & -k) dat[k - 1] = AbelGroup::op(dat[k - 1], x);
  }

  void add(int k, E x) { multiply(k, x); }

  template <class F>
  int max_right(F& check) {
    assert(check(E(0)));
    ll i = 0;
    E s = AbelGroup::unit();
    int k = 1;
    int N = dat.size() + 1;
    while (2 * k < N) k *= 2;
    while (k) {
      if (i + k < N && check(AbelGroup::op(s, dat[i + k - 1]))) {
        i += k;
        s = AbelGroup::op(s, dat[i - 1]);
      }
      k >>= 1;
    }
    return i;
  }

  int find_kth(E k) {
    auto check = [&](E x) -> bool { return x <= k; };
    return max_right(check);
  }

  void debug() { print("fenwick", dat); }
};
#line 1 "/home/maspy/compro/library/ds/mo.hpp"
struct Mo {
  vector<pair<int, int> > lr;

  void add(int l, int r) { /* [l, r) */
    lr.emplace_back(l, r);
  }

  template <typename AL, typename AR, typename EL, typename ER, typename O>
  void calc(const AL &add_left, const AR &add_right, const EL &erase_left,
            const ER &erase_right, const O &query) {
    int n = 1;
    for (auto &&[l, r]: lr) chmax(n, r);
    int q = (int)lr.size();
    int bs = n / min<int>(n, sqrt(q));
    vector<int> ord(q);
    iota(begin(ord), end(ord), 0);
    sort(begin(ord), end(ord), [&](int a, int b) {
      int ablock = lr[a].first / bs, bblock = lr[b].first / bs;
      if (ablock != bblock) return ablock < bblock;
      return (ablock & 1) ? lr[a].second > lr[b].second
                          : lr[a].second < lr[b].second;
    });
    int l = 0, r = 0;
    for (auto idx: ord) {
      while (l > lr[idx].first) add_left(--l);
      while (r < lr[idx].second) add_right(r++);
      while (l < lr[idx].first) erase_left(l++);
      while (r > lr[idx].second) erase_right(--r);
      query(idx);
    }
  }

  template <typename A, typename E, typename O>
  void calc(const A &add, const E &erase, const O &query) {
    calc(add, add, erase, erase, query);
  }
};
#line 5 "main.cpp"

#line 2 "/home/maspy/compro/library/ds/lazysegtree.hpp"

template <typename Lazy>
struct LazySegTree {
  using Monoid_X = typename Lazy::X_structure;
  using Monoid_A = typename Lazy::A_structure;
  using X = typename Monoid_X::value_type;
  using A = typename Monoid_A::value_type;
  int n, log, size;
  vc<X> dat;
  vc<A> laz;

  LazySegTree() : LazySegTree(0) {}
  LazySegTree(int n) : LazySegTree(vc<X>(n, Monoid_X::unit())) {}
  LazySegTree(vc<X> v) : n(len(v)) {
    log = 1;
    while ((1 << log) < n) ++log;
    size = 1 << log;
    dat.assign(size << 1, Monoid_X::unit());
    laz.assign(size, Monoid_A::unit());
    FOR(i, n) dat[size + i] = v[i];
    FOR3_R(i, 1, size) update(i);
  }

  template <typename F>
  LazySegTree(int n, F f) : n(n) {
    log = 1;
    while ((1 << log) < n) ++log;
    size = 1 << log;
    dat.assign(size << 1, Monoid_X::unit());
    laz.assign(size, Monoid_A::unit());
    FOR(i, n) dat[size + i] = f(i);
    FOR3_R(i, 1, size) update(i);
  }

  void reset() {
    fill(all(dat), Monoid_X::unit());
    fill(all(laz), Monoid_A::unit());
  }

  void reset(const vc<X>& v) {
    assert(len(v) == n);
    reset();
    FOR(i, n) dat[size + i] = v[i];
    FOR3_R(i, 1, size) update(i);
  }

  void update(int k) { dat[k] = Monoid_X::op(dat[2 * k], dat[2 * k + 1]); }

  void all_apply(int k, A a) {
    dat[k] = Lazy::act(dat[k], a);
    if (k < size) laz[k] = Monoid_A::op(laz[k], a);
  }

  void push(int k) {
    all_apply(2 * k, laz[k]);
    all_apply(2 * k + 1, laz[k]);
    laz[k] = Monoid_A::unit();
  }

  void set(int p, X x) {
    assert(0 <= p && p < n);
    p += size;
    for (int i = log; i >= 1; i--) push(p >> i);
    dat[p] = x;
    for (int i = 1; i <= log; i++) update(p >> i);
  }

  X get(int p) {
    assert(0 <= p && p < n);
    p += size;
    for (int i = log; i >= 1; i--) push(p >> i);
    return dat[p];
  }

  vc<X> get_all() {
    FOR(i, size) push(i);
    return {dat.begin() + size, dat.begin() + size + n};
  }

  X prod(int l, int r) {
    assert(0 <= l && l <= r && r <= n);
    if (l == r) return Monoid_X::unit();

    l += size;
    r += size;

    for (int i = log; i >= 1; i--) {
      if (((l >> i) << i) != l) push(l >> i);
      if (((r >> i) << i) != r) push((r - 1) >> i);
    }

    X xl = Monoid_X::unit(), xr = Monoid_X::unit();
    while (l < r) {
      if (l & 1) xl = Monoid_X::op(xl, dat[l++]);
      if (r & 1) xr = Monoid_X::op(dat[--r], xr);
      l >>= 1;
      r >>= 1;
    }

    return Monoid_X::op(xl, xr);
  }

  X prod_all() { return dat[1]; }

  void apply(int p, A a) {
    assert(0 <= p && p < n);
    p += size;
    dat[p] = Lazy::act(dat[p], a);
    for (int i = 1; i <= log; i++) update(p >> i);
  }

  void apply(int l, int r, A a) {
    assert(0 <= l && l <= r && r <= n);
    if (l == r) return;

    l += size;
    r += size;

    for (int i = log; i >= 1; i--) {
      if (((l >> i) << i) != l) push(l >> i);
      if (((r >> i) << i) != r) push((r - 1) >> i);
    }

    {
      int l2 = l, r2 = r;
      while (l < r) {
        if (l & 1) all_apply(l++, a);
        if (r & 1) all_apply(--r, a);
        l >>= 1;
        r >>= 1;
      }
      l = l2;
      r = r2;
    }

    for (int i = 1; i <= log; i++) {
      if (((l >> i) << i) != l) update(l >> i);
      if (((r >> i) << i) != r) update((r - 1) >> i);
    }
  }

  template <typename C>
  int max_right(C& check, int l) {
    assert(0 <= l && l <= n);
    assert(check(Monoid_X::unit()));
    if (l == n) return n;
    l += size;
    for (int i = log; i >= 1; i--) push(l >> i);
    X sm = Monoid_X::unit();
    do {
      while (l % 2 == 0) l >>= 1;
      if (!check(Monoid_X::op(sm, dat[l]))) {
        while (l < size) {
          push(l);
          l = (2 * l);
          if (check(Monoid_X::op(sm, dat[l]))) {
            sm = Monoid_X::op(sm, dat[l]);
            l++;
          }
        }
        return l - size;
      }
      sm = Monoid_X::op(sm, dat[l]);
      l++;
    } while ((l & -l) != l);
    return n;
  }

  template <typename C>
  int min_left(C& check, int r) {
    assert(0 <= r && r <= n);
    assert(check(Monoid_X::unit()));
    if (r == 0) return 0;
    r += size;
    for (int i = log; i >= 1; i--) push((r - 1) >> i);
    X sm = Monoid_X::unit();
    do {
      r--;
      while (r > 1 && (r % 2)) r >>= 1;
      if (!check(Monoid_X::op(dat[r], sm))) {
        while (r < size) {
          push(r);
          r = (2 * r + 1);
          if (check(Monoid_X::op(dat[r], sm))) {
            sm = Monoid_X::op(dat[r], sm);
            r--;
          }
        }
        return r + 1 - size;
      }
      sm = Monoid_X::op(dat[r], sm);
    } while ((r & -r) != r);
    return 0;
  }

  void debug() { print("lazysegtree getall:", get_all()); }
};
#line 2 "/home/maspy/compro/library/alg/monoid_min.hpp"
template <class X>
struct Monoid_Min {
  using value_type = X;
  static constexpr X op(const X &x, const X &y) noexcept { return min(x, y); }
  static constexpr X unit() { return numeric_limits<X>::max(); }
  static constexpr bool commute = true;
};
#line 3 "/home/maspy/compro/library/alg/lazy_min_add.hpp"

template <typename E>
struct Lazy_Min_Add {
  using MX = Monoid_Min<E>;
  using MA = Group_Add<E>;
  using X_structure = MX;
  using A_structure = MA;
  using X = typename MX::value_type;
  using A = typename MA::value_type;
  static constexpr X act(const X &x, const A &a) {
    if (x == numeric_limits<E>::max()) return x;
    return x + a;
  }
};
#line 8 "main.cpp"

void solve() {
  LL(N, Q);
  VEC(ll, A, N);
  for (auto&& x: A) --x;
  VEC(pi, query, Q);
  for (auto&& [a, b]: query) --a;

  vi ANS(Q);
  FenwickTree<Group_Add<int>> bit_l(N), bit_r(N);
  LazySegTree<Lazy_Min_Add<int>> seg(N, [&](int i) -> int { return 0; });
  ll inv_l = 0, inv_r = 0, inv_lr = 0;
  for (auto&& x: A) {
    inv_r += bit_r.sum(x + 1, N);
    bit_r.add(x, 1);
    seg.apply(x + 1, N, 1);
  }

  Mo mo;
  FOR(q, Q) {
    auto [l, r] = query[q];
    mo.add(l, r);
  }

  auto ADD_L = [&](int i) -> void {
    int x = A[i];
    inv_l -= bit_l.sum(x + 1, N);
    inv_lr -= bit_r.sum(x);
    bit_l.add(x, -1);
    seg.apply(0, x, -1);
  };
  auto ADD_R = [&](int i) -> void {
    int x = A[i];
    inv_r -= bit_r.sum(x);
    inv_lr -= bit_l.sum(x + 1, N);
    bit_r.add(x, -1);
    seg.apply(x + 1, N, -1);
  };
  auto RM_L = [&](int i) -> void {
    int x = A[i];
    inv_l += bit_l.sum(x + 1, N);
    inv_lr += bit_r.sum(x);
    bit_l.add(x, 1);
    seg.apply(0, x, 1);
  };
  auto RM_R = [&](int i) -> void {
    int x = A[i];
    inv_r += bit_r.sum(x);
    inv_lr += bit_l.sum(x + 1, N);
    bit_r.add(x, 1);
    seg.apply(x + 1, N, 1);
  };
  auto CALC = [&](int q) -> void {
    auto [L, R] = query[q];
    ll inv = inv_l + inv_r + inv_lr;
    ANS[q] = inv + seg.prod_all() * (R - L);
  };
  mo.calc(ADD_L, ADD_R, RM_L, RM_R, CALC);
  for (auto&& x: ANS) print(x);
}

signed main() {
  cout << fixed << setprecision(15);

  ll T = 1;
  // LL(T);
  FOR(T) solve();

  return 0;
}