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# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Runtime.CompilerServices;
using System.Text;
using static Template;
using static System.Console;
using static System.Convert;
using static System.Math;
using Pi = Pair<int, int>;
using Number = System.Int64;

class Solver
{
    public void Solve()
    {
        int n, q;
        Input.Make(out n, out q);
        var seg = new LazySegmentTree<long, long>(n, 0, 0, (a, b) => a + b, (a, b) => a + b, (a, b) => a + b, (a, b) => a * b);
        while (q-- > 0)
        {
            int c = Input.Next<int>();
            if (c == 0)
            {
                int s, t, x;
                Input.Make(out s, out t, out x);
                seg.Update(s-1, t, x);
            }
            else
            {
                int s, t;
                Input.Make(out s, out t);
                WriteLine(seg.Query(s-1, t));
            }
        }
    }
}

public class LazySegmentTree<T,E>
    where E : IComparable<E>
{
    protected readonly int num;
    protected readonly T minT;
    protected readonly T[] item;
    protected readonly E minE;
    protected readonly E[] lazy;
    protected readonly Func<T, T, T> func;
    protected readonly Func<T, E, T> updateFunc;
    protected readonly Func<E, E, E> lazyFunc;
    protected readonly Func<E, int, E> secf;

    public T this[int i]
    {
        get { return item[i + num - 1]; }
        set { item[i + num - 1] = value; }
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    protected int Parent(int index)
        => (index - 1) >> 1;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    protected int Left(int index)
        => (index << 1) + 1;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    protected int Right(int index)
        => (index + 1) << 1;
    public LazySegmentTree(int num, T minT, E minE, Func<T, T, T> func, Func<T, E, T> updateFunc = null, Func<E, E, E> lazyFunc = null, Func<E, int, E> secf = null)
    {
        this.func = func;
        this.num = 1;
        this.minT = minT;
        this.minE = minE;
        this.updateFunc = updateFunc ?? ((a, b) => a);
        this.lazyFunc = lazyFunc ?? ((a, b) => b);
        this.secf = secf ?? ((a, b) => a);

        while (this.num <= num)
            this.num <<= 1;
        item = new T[2 * this.num - 1];
        for (var i = 0; i < 2 * this.num - 1; i++)
            item[i] = minT;
        lazy = Enumerable.Repeat(0, 2 * this.num + 1).Select(_ => minE).ToArray();
    }
    protected void eval(int len, int k)
    {
        if (lazy[k].CompareTo(minE) == 0) return;
        if (Right(k) < num * 2)
        {
            lazy[Left(k)] = lazyFunc(lazy[Left(k)], lazy[k]);
            lazy[Right(k)] = lazyFunc(lazy[Right(k)], lazy[k]);
        }
        item[k] = updateFunc(item[k], secf(lazy[k], len));
        lazy[k] = minE;
    }
    public void Update(int left, int right, E value)
        => Update(left, right, 0, 0, num, value);
    protected void Update(int left, int right, int k, int l, int r, E value)
    {
        eval(r - l, k);
        if (r <= left || right <= l) return;
        if (left <= l && r <= right)
        {
            lazy[k] = lazyFunc(lazy[k], value);
            eval(r - l, k);
        }
        else
        {
            Update(left, right, Left(k), l, (l + r) >> 1, value);
            Update(left, right, Right(k), (l + r) >> 1, r, value);
            item[k] = func(item[Left(k)], item[Right(k)]);
        }
    }
    public T Query(int left, int right)
        => Query(left, right, 0, 0, num);
    protected T Query(int left, int right, int k, int l, int r)
    {
        if (r <= left || right <= l) return minT;
        eval(r - l, k);
        if (left <= l && r <= right) return item[k];
        else
            return func(Query(left, right, Left(k), l, (l + r) >> 1), Query(left, right, Right(k), (l + r) >> 1, r));
    }
}

#region Template
public class Template
{
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmin<T>(ref T num, T val) where T : IComparable<T>
    { if (num.CompareTo(val) == 1) { num = val; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmax<T>(ref T num, T val) where T : IComparable<T>
    { if (num.CompareTo(val) == -1) { num = val; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static void swap<T>(ref T v1, ref T v2)
    { var t = v2; v2 = v1; v1 = t; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static T[] Create<T>(int n, Func<T> f)
        => Enumerable.Repeat(0, n).Select(_ => f()).ToArray();
    public static void Fail() => Fail("No");
    public static void Fail<T>(T s) { Console.WriteLine(s); Console.Out.Close(); Environment.Exit(0); }
    static void Main(string[] args)
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        var p = new Solver();
        for (var i = 1; i > 0; --i)
            p.Solve();
        Console.Out.Flush();
    }
}

public class Input
{
    public static string read => Console.ReadLine().Trim();
    public static int[] ar => read.Split(' ').Select(int.Parse).ToArray();
    public static int num => Convert.ToInt32(read);
    public static long[] arL => read.Split(' ').Select(long.Parse).ToArray();
    public static long numL => Convert.ToInt64(read);
    public static char[][] grid(int h)
        => Create(h, () => read.ToCharArray());
    public static int[] ar1D(int n)
        => Create(n, () => num);
    public static long[] arL1D(int n)
        => Create(n, () => numL);
    public static string[] strs(int n)
        => Create(n, () => read);
    public static int[][] ar2D(int n)
        => Create(n, () => ar);
    public static long[][] arL2D(int n)
        => Create(n, () => arL);
    public static List<T>[] edge<T>(int n)
        => Create(n, () => new List<T>());
    public static void Make<T1, T2>(out T1 v1, out T2 v2)
    {
        v1 = Next<T1>();
        v2 = Next<T2>();
    }
    public static void Make<T1, T2, T3>(out T1 v1, out T2 v2, out T3 v3)
    {
        Make(out v1, out v2);
        v3 = Next<T3>();
    }
    public static void Make<T1, T2, T3, T4>(out T1 v1, out T2 v2, out T3 v3, out T4 v4)
    {
        Make(out v1, out v2, out v3);
        v4 = Next<T4>();
    }
    public static void Make<T1, T2, T3, T4, T5>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5)
    {
        Make(out v1, out v2, out v3, out v4);
        v5 = Next<T5>();
    }
    public static void Make<T1, T2, T3, T4, T5, T6>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6)
    {
        Make(out v1, out v2, out v3, out v4, out v5);
        v6 = Next<T6>();
    }
    static Input()
    {
        sc = new Queue<string>();
        dic = new Dictionary<Type, Func<string, object>>();
        dic[typeof(int)] = s => int.Parse(s);
        dic[typeof(long)] = s => long.Parse(s);
        dic[typeof(char)] = s => char.Parse(s);
        dic[typeof(double)] = s => double.Parse(s);
        dic[typeof(uint)] = s => uint.Parse(s);
        dic[typeof(ulong)] = s => ulong.Parse(s);
        dic[typeof(string)] = s => s;
    }
    private static Dictionary<Type, Func<string, object>> dic;
    private static Queue<string> sc;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static T Next<T>() { if (sc.Count == 0) foreach (var item in read.Split(' ')) sc.Enqueue(item); return (T)dic[typeof(T)](sc.Dequeue()); }
    public const int MOD = 1000000007;
}

public class Pair<T1, T2> : IComparable<Pair<T1, T2>>
{
    public T1 v1;
    public T2 v2;
    public Pair() { v1 = default(T1);v2 = default(T2); }
    public Pair(T1 v1, T2 v2)
    { this.v1 = v1; this.v2 = v2; }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public int CompareTo(Pair<T1, T2> p)
    {
        var c = Comparer<T1>.Default.Compare(v1, p.v1);
        if (c == 0)
            c = Comparer<T2>.Default.Compare(v2, p.v2);
        return c;
    }
    public override string ToString()
        => $"{v1.ToString()} {v2.ToString()}";
}

public class Pair<T1, T2, T3> : Pair<T1, T2>, IComparable<Pair<T1, T2, T3>>
{
    public T3 v3;
    public Pair() : base() { v3 = default(T3); }
    public Pair(T1 v1, T2 v2, T3 v3) : base(v1, v2)
    { this.v3 = v3; }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public int CompareTo(Pair<T1, T2, T3> p)
    {
        var c = base.CompareTo(p);
        if (c == 0)
            c = Comparer<T3>.Default.Compare(v3, p.v3);
        return c;
    }
    public override string ToString()
        => $"{base.ToString()} {v3.ToString()}";
}
#endregion