Problem:
RSQ and RAQ

Write a program which manipulates a sequence A = {a1, a2, . . . , an} with the following operations:

add(s, t, x): add x to as, as+1, ..., at.

getSum(s, t): report the sum of as, as+1, ..., at.

Note that the initial values of ai (i = 1, 2, . . . , n) are 0.

Input

n q
query1
query2
:
queryq

In the first line, n (the number of elements in A) and q (the number of queries) are given. Then, ith query queryi is given in the following format:

0 s t x

or

1 s t

The first digit represents the type of the query. '0' denotes add(s, t, x) and '1' denotes getSum(s, t).

Output

For each getSum operation, print the sum;

Constraints

1 ≤ n ≤ 100000

1 ≤ q ≤ 100000

1 ≤ s ≤ t ≤ n

0 ≤ x < 1000

Sample Input 1

3 5
0 1 2 1
0 2 3 2
0 3 3 3
1 1 2
1 2 3

Sample Output 1

4
8

Sample Input 2

4 3
1 1 4
0 1 4 1
1 1 4

Sample Output 2

0
4

Solution in C++14 (judge verdict: Accepted)

#include <bits/stdc++.h>

using namespace std;

#define pb push_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define all(a) (a).begin(),(a).end()
#define endl "\n"
#define rep(i, a, b) for (auto (i) = (a); (i) < (b); (i)++)
#define rrep(i, a, b) for (auto (i) = (a); (i) > (b); (i)--)
#define UNIQUE(v) (v).erase(unique((v).begin(), (v).end()), (v).end());

#ifdef LOCAL_DEFINE
struct InitInput{
  InitInput() {
    FILE *stream1;
    stream1=freopen("/Users/aim_cpo/CLionProjects/competitive/in.txt","r",stdin);
    assert(stream1 != nullptr);
    cerr << "This problem is not interactive" << endl;
  }
}LOCAL_INPUT;
struct LOCAL_OUTPUT{
  LOCAL_OUTPUT() {
    FILE *stream2;
    const char *outputfile = "out.txt";
    stream2 = freopen(outputfile, "w", stdout);
    assert(stream2 != nullptr);
    cerr << "output [ " << outputfile << " ]" << endl;
  }
}/*LOCAL_OUTPUT*/;
#define show(x) cerr << #x << " = " << (x) << " (line " << __LINE__ << ")" << endl
#define showV(v, n) do{\
for(int _i_t_e_=0; _i_t_e_<(n);_i_t_e_++)\
cerr<<"("<<_i_t_e_<<" = "<<(v)[_i_t_e_]<<") ";\
cerr<<endl;}while(0)
#define showA(a, n) do{\
for(int _i_t_e_=0;_i_t_e_<(n);_i_t_e_++)\
cerr<<"("<<_i_t_e_<<" = "<<(a)[_i_t_e_]<<") ";\
cerr<<endl;}while(0)
#define showA2(a, n, m) do{\
for(int _i_t_e_=0;_i_t_e_<(n);_i_t_e_++){\
for(int _i_t_e_2=0;_i_t_e_2<(m);_i_t_e_2++){\
cerr<<"("<<_i_t_e_<<", "<<_i_t_e_2<<" = "<<(a)[_i_t_e_][_i_t_e_2]<<") ";\
}cerr<<endl;}cerr<<endl;}while(0)
#else
#define show(x)
#define showV(v, n)
#define showA(a, n)
#define showA2(a, n, m)
#endif

struct InitAim{
  InitAim() {
    ios::sync_with_stdio(false);cin.tie(nullptr);
    cout.precision(12);cout<<fixed;
#ifdef LOCAL_DEFINE
    cerr << "This problem is not interactive" << endl;
#endif
  }
}aim_cpo;

typedef long long ll;
typedef unsigned long long ull;

constexpr const int INT_INF=0x3f3f3f3f; //1061109567
constexpr const ll LL_INF=0x3f3f3f3f3f3f3f3f; //4557430888798830399

template <typename T> bool chmin(T &a, T b){return a>b?(a=b,true):false;}
template <typename T> bool chmax(T &a, T b){return a<b?(a=b,true):false;}
template <typename T> void ln(T i, T n){cout<<(i==n-1?"\n":" ");}
template<typename T, typename S>
ostream &operator<<(ostream &out, const pair<T, S> &pair1) {
  out << '(' << pair1.fi << ", " << pair1.se << ')';
  return out;
}
template<typename T>
ostream &operator<<(ostream &out, const vector<T> &vector1) {
  out << '[';
  for (unsigned int i = 0; i < vector1.size(); i++) {
    out << vector1[i];
    if (i == vector1.size() - 1)out << "]"; else out << ", ";
  }
  return out;
}

// INT
#define GCD(a, b) __gcd(a, b)
template <typename T> T LCM(T a, T b) {return a / GCD(a, b) * b;}
template <typename T> T EXTGCD(T a, T b, T& x, T& y) {
  T d = a;
  if (b != 0) {d=EXTGCD(b,a%b,y,x);y-=(a/b)*x;}
  else x=1,y=0;
  return d;
}
template <typename T> bool is_prime(T a) {
  for(int i=2;i*i<=a;i++)if(a%i==0)return true;
  return false;
}
template <typename T, typename S> T Pow(T a, S b) {
  T res = 1, now = a;
  while(b){if(b&1)res*=now;b>>=1;now*=now;}return res;
}

// MOD
ll MOD = 1000000000L + 7L;
#define add(a, b) ((a % MOD) + (b % MOD)) % MOD
#define mul(a, b) ((a % MOD) * (b % MOD)) % MOD
#define sub(a, b) ((a % MOD) + MOD - (b % MOD)) % MOD
template <typename T, typename S> T ModPow(T a, S b) {
  T res = 1, now = a;
  while(b){if(b&1)res=mul(res,now);b>>=1;now=mul(now,now);}return res;
}
template <typename T> T mod_inverse(T a, T mod, bool prime){ // if mod is prime, "prime" is true.
  if(prime)return ModPow(a, mod - 2);
  else{T x,y;EXTGCD(a,mod,x,y);return (mod+x%mod)%mod;}
}
#define divide(a, b) ((a % MOD) * (mod_inverse(b, MOD, true))) % MOD

//LLの数値をつかう時は最後にLLをつける癖をつけよう
///////////////////////////////////////////////////////////////////////////////////
// VARIABLE
///////////////////////////////////////////////////////////////////////////////////

int n, q;

///////////////////////////////////////////////////////////////////////////////////
// TEMPLATE(data structure)
///////////////////////////////////////////////////////////////////////////////////

template <typename T, typename S = T>
class LazyIntervalTree {
    using F = function<T(T, T)>;
    using G = function<T(T, S, int)>;
    using H = function<S(S, S)>;
public:
    LazyIntervalTree(int n, const F f, const G g, const H h, const T &init, const S OM)
    : f(f), g(g), h(h), init(init), OM(OM) {
      size = 1;
      while (size < n) size <<= 1;
      data.assign(2 * size, init);
      lazy.assign(2 * size, OM);
    }
    void set(int k, const T &x) {
      data[k + size] = x;
    }
    void build() {
      for (int i = size - 1; i > 0; i--) {
        data[i] = f(data[2 * i], data[2 * i + 1]);
      }
    }
    void propagate(int k, int len) {
      if (lazy[k] != OM) {
        if (k < size) {
          lazy[2 * k] = h(lazy[2 * k], lazy[k]);
          lazy[2 * k + 1] = h(lazy[2 * k + 1], lazy[k]);
        }
        data[k] = g(data[k], lazy[k], len);
        lazy[k] = OM;
      }
    }
    T update(int a, int b, const S &x, int k, int l, int r) {
      propagate(k, r - l);
      if (r <= a || b <= l) {
        return data[k];
      } else if (a <= l && r <= b) {
        lazy[k] = h(lazy[k], x);
        propagate(k, r - l);
        return data[k];
      } else {
        return data[k] = f(update(a, b, x, 2 * k, l, (l + r) >> 1),
          update(a, b, x, 2 * k + 1, (l + r) >> 1, r));
      }
    }
    T update(int a, int b, const S &x) {
      return update(a, b, x, 1, 0, size);
    }
    T query(int a, int b, int k, int l, int r) {
      propagate(k, r - l);
      if (r <= a || b <= l) {
        return init;
      } else if (a <= l && r <= b) {
        return data[k];
      } else {
        return f(query(a, b, 2 * k, l, (l + r) >> 1),
          query(a, b, 2 * k + 1, (l + r) >> 1, r));
      }
    }
    T query(int a, int b) {
      return query(a, b, 1, 0, size);
    }
    T operator[](const int &k) {
      return query(k, k + 1);
    }
    void showLazy() {
      for (int i = 0; i < n; i++) {
        cerr << lazy[i + size] << " ";
      }
      cerr << endl;
    }
private:
    int size;
    vector <T> data;
    vector <S> lazy;
    const F f;
    const G g;
    const H h;
    const T init;
    const S OM;
};

///////////////////////////////////////////////////////////////////////////////////
// MAIN
///////////////////////////////////////////////////////////////////////////////////

int main() {
  cin >> n >> q;
  LazyIntervalTree<ll, ll> seg(n, [](ll a, ll b){return a + b;},
    [](ll a, ll b, int c){return a + b * c;},
    [](ll a, ll b){return a + b;},
    0, 0);
  rep(i, 0, n) seg.set(i, 0);
  seg.build();
  rep(i, 0, q) {
    int a; cin >> a;
    if (a) {
      int l, r; cin >> l >> r; l--; r--;
      cout << seg.query(l, r + 1) << endl;
    } else {
      int l, r; ll x; cin >> l >> r >> x; l--; r--;
      seg.update(l, r + 1, x);
    }
  }
#ifdef LOCAL_DEFINE
  cerr << "Time elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC << "s." << endl;
  show(MOD);
#endif
  return 0;
}

///////////////////////////////////////////////////////////////////////////////////
// NOTE
///////////////////////////////////////////////////////////////////////////////////