:warning: よく使う Lazy Segment Tree
(segment-tree/lazy-segment-tree-util.hpp)

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#pragma once
#include "segment-tree/lazy-segment-tree.hpp"

namespace LazySegmentTreeUtil {
template <class T>
T Zero() { return T{}; }
template <class T>
T One() { return T{1}; }
template <class T, T e>
T Const() { return e; }
template <class T>
T Add(T x, T y) { return x + y; }
template <class T>
T Mul(T x, T y) { return x * y; }
template <class T>
T Max(T x, T y) { return x > y ? x : y; }
template <class T>
T Min(T x, T y) { return x < y ? x : y; }
template <class T>
using P = pair<T, T>;
template <class T>
P<T> PAdd(P<T> x, P<T> y) { return P<T>{x.first + y.first, x.second + y.second}; }
template <class T>
P<T> FPAdd(T f, P<T> x) { return P<T>{x.first, x.second + x.first * f}; }
template <class T>
P<T> PZero() { return P<T>{T{}, T{}}; }
template <class T>
vector<P<T>> InitPair(const vector<T>& a) {
  vector<P<T>> v(a.size());
  for (int i = 0; i < (int)v.size(); i++) v[i] = P<T>{1, a[i]};
  return v;
}
template <class T>
struct LazySegmentTreeAddSum : LazySegmentTree<P<T>, PAdd<T>, PZero<T>, T, FPAdd<T>, Add<T>, Zero<T>> {
  using base = LazySegmentTree<P<T>, PAdd<T>, PZero<T>, T, PAdd<T>, Add<T>, Zero<T>>;
  LazySegmentTreeAddSum(int n) : base(vector<P<T>>(n, PZero<T>())) {}
  LazySegmentTreeAddSum(const vector<T>& a) : base(InitPair(a)) {}
};
template <class T>
struct LazySegmentTreeMulSum : LazySegmentTree<T, Add<T>, Zero<T>, T, Mul<T>, Mul<T>, One<T>> {
  using base = LazySegmentTree<T, Add<T>, Zero<T>, T, Mul<T>, Mul<T>, One<T>>;
  LazySegmentTreeMulSum(int n) : base(vector<T>(n, Zero<T>())) {}
  LazySegmentTreeMulSum(const vector<T>& a) : base(a) {}
};
};  // namespace LazySegmentTreeUtil
using LazySegmentTreeUtil::LazySegmentTreeAddSum;
using LazySegmentTreeUtil::LazySegmentTreeMulSum;
/**
 * @brief よく使う Lazy Segment Tree
 * @docs docs/segment-tree/lazy-segment-tree-util.md
 */
#line 2 "segment-tree/lazy-segment-tree.hpp"

template <class T, T (*op)(T, T), T (*e)(), class F, T (*mapping)(F, T), F (*composition)(F, F), F (*id)()>
struct LazySegmentTree {
 private:
  int _n, size, log;
  vector<T> d;
  vector<F> lz;

  void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
  void all_apply(int k, F f) {
    d[k] = mapping(f, d[k]);
    if (k < size) lz[k] = composition(f, lz[k]);
  }
  void push(int k) {
    all_apply(2 * k, lz[k]);
    all_apply(2 * k + 1, lz[k]);
    lz[k] = id();
  }

 public:
  LazySegmentTree() : LazySegmentTree(0) {}
  explicit LazySegmentTree(int n) : LazySegmentTree(vector<T>(n, e())) {}
  explicit LazySegmentTree(const vector<T>& v) : _n(int(v.size())) {
    size = 1, log = 0;
    while (size < _n) size <<= 1, log++;
    d = vector<T>(2 * size, e());
    lz = vector<F>(size, id());
    for (int i = 0; i < _n; i++) d[size + i] = v[i];
    for (int i = size - 1; i > 0; i--) update(i);
  }

  void set(int p, T x) {
    assert(0 <= p && p < _n);
    p += size;
    for (int i = log; i >= 1; i--) push(p >> i);
    d[p] = x;
    for (int i = 1; i <= log; i++) update(p >> i);
  }
  T get(int p) {
    assert(0 <= p && p < _n);
    p += size;
    for (int i = log; i >= 1; i--) push(p >> i);
    return d[p];
  }
  T prod(int l, int r) {
    assert(0 <= l && l <= r && r <= _n);
    if (l == r) return e();
    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);
    }
    T sml = e(), smr = e();
    while (l < r) {
      if (l & 1) sml = op(sml, d[l++]);
      if (r & 1) smr = op(d[--r], smr);
      l >>= 1, r >>= 1;
    }
    return op(sml, smr);
  }
  T all_prod() { return d[1]; }
  void apply(int p, F f) {
    assert(0 <= p && p < _n);
    p += size;
    for (int i = log; i >= 1; i--) push(p >> i);
    d[p] = mapping(f, d[p]);
    for (int i = 1; i <= log; i++) update(p >> i);
  }
  void apply(int l, int r, F f) {
    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++, f);
        if (r & 1) all_apply(--r, f);
        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 <bool (*g)(T)>
  int max_right(int l) {
    return max_right(l, [](T x) { return g(x); });
  }
  template <class G>
  int max_right(int l, G g) {
    assert(0 <= l && l <= _n);
    assert(g(e()));
    if (l == _n) return _n;
    l += size;
    for (int i = log; i >= 1; i--) push(l >> i);
    T sm = e();
    do {
      while (l % 2 == 0) l >>= 1;
      if (!g(op(sm, d[l]))) {
        while (l < size) {
          push(l);
          l = (2 * l);
          if (g(op(sm, d[l]))) sm = op(sm, d[l++]);
        }
        return l - size;
      }
      sm = op(sm, d[l++]);
    } while ((l & -l) != l);
    return _n;
  }

  template <bool (*g)(T)>
  int min_left(int r) {
    return min_left(r, [](T x) { return g(x); });
  }
  template <class G>
  int min_left(int r, G g) {
    assert(0 <= r && r <= _n);
    assert(g(e()));
    if (r == 0) return 0;
    r += size;
    for (int i = log; i >= 1; i--) push((r - 1) >> i);
    T sm = e();
    do {
      r--;
      while (r > 1 && (r % 2)) r >>= 1;
      if (!g(op(d[r], sm))) {
        while (r < size) {
          push(r);
          r = (2 * r + 1);
          if (g(op(d[r], sm))) sm = op(d[r--], sm);
        }
        return r + 1 - size;
      }
      sm = op(d[r], sm);
    } while ((r & -r) != r);
    return 0;
  }
};

/**
 * @brief Lazy Segment Tree
 * @docs docs/segment-tree/lazy-segment-tree.md
 */
#line 3 "segment-tree/lazy-segment-tree-util.hpp"

namespace LazySegmentTreeUtil {
template <class T>
T Zero() { return T{}; }
template <class T>
T One() { return T{1}; }
template <class T, T e>
T Const() { return e; }
template <class T>
T Add(T x, T y) { return x + y; }
template <class T>
T Mul(T x, T y) { return x * y; }
template <class T>
T Max(T x, T y) { return x > y ? x : y; }
template <class T>
T Min(T x, T y) { return x < y ? x : y; }
template <class T>
using P = pair<T, T>;
template <class T>
P<T> PAdd(P<T> x, P<T> y) { return P<T>{x.first + y.first, x.second + y.second}; }
template <class T>
P<T> FPAdd(T f, P<T> x) { return P<T>{x.first, x.second + x.first * f}; }
template <class T>
P<T> PZero() { return P<T>{T{}, T{}}; }
template <class T>
vector<P<T>> InitPair(const vector<T>& a) {
  vector<P<T>> v(a.size());
  for (int i = 0; i < (int)v.size(); i++) v[i] = P<T>{1, a[i]};
  return v;
}
template <class T>
struct LazySegmentTreeAddSum : LazySegmentTree<P<T>, PAdd<T>, PZero<T>, T, FPAdd<T>, Add<T>, Zero<T>> {
  using base = LazySegmentTree<P<T>, PAdd<T>, PZero<T>, T, PAdd<T>, Add<T>, Zero<T>>;
  LazySegmentTreeAddSum(int n) : base(vector<P<T>>(n, PZero<T>())) {}
  LazySegmentTreeAddSum(const vector<T>& a) : base(InitPair(a)) {}
};
template <class T>
struct LazySegmentTreeMulSum : LazySegmentTree<T, Add<T>, Zero<T>, T, Mul<T>, Mul<T>, One<T>> {
  using base = LazySegmentTree<T, Add<T>, Zero<T>, T, Mul<T>, Mul<T>, One<T>>;
  LazySegmentTreeMulSum(int n) : base(vector<T>(n, Zero<T>())) {}
  LazySegmentTreeMulSum(const vector<T>& a) : base(a) {}
};
};  // namespace LazySegmentTreeUtil
using LazySegmentTreeUtil::LazySegmentTreeAddSum;
using LazySegmentTreeUtil::LazySegmentTreeMulSum;
/**
 * @brief よく使う Lazy Segment Tree
 * @docs docs/segment-tree/lazy-segment-tree-util.md
 */
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