Problem:
Score : 100 points

Problem Statement

You are given an array a_0, a_1, ..., a_{N-1} of length N. Process Q queries of the following types.

0 p x: a_p \gets a_p + x

1 l r: Print \sum_{i = l}^{r - 1}{a_i}.

Constraints

1 \leq N, Q \leq 500,000

0 \leq a_i, x \leq 10^9

0 \leq p < N

0 \leq l_i < r_i \leq N

All values in Input are integer.

Input

Input is given from Standard Input in the following format:

N Q
a_0 a_1 ... a_{N - 1}
\textrm{Query}_0
\textrm{Query}_1
:
\textrm{Query}_{Q - 1}

Output

For each query of the latter type, print the answer.

Sample Input 1

5 5
1 2 3 4 5
1 0 5
1 2 4
0 3 10
1 0 5
1 0 3

Sample Output 1

15
7
25
6

Solution in C# (.NET Core 3.1.201) (judge verdict: Accepted)

using AtCoder;
using AtCoder.Internal;
using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Numerics;
using System.Runtime.CompilerServices;
using System.Runtime.Intrinsics.X86;

class Program
{
    static void Main(string[] args)
    {
        int n, q;
        var line = Console.ReadLine().Split();
        n = int.Parse(line[0]);
        q = int.Parse(line[1]);

        var fw = new LongFenwickTree(n);
        line = Console.ReadLine().Split();
        int[] a = line.Select(int.Parse).ToArray();
        for (int i = 0; i < a.Length; i++)
        {
            fw.Add(i, a[i]);
        }

        for (int i = 0; i < q; i++)
        {
            var query = Console.ReadLine().Split().Select(int.Parse).ToArray();
            if (query[0] == 0)
            {
                fw.Add(query[1], query[2]);
            }
            else
            {
                Console.WriteLine(fw.Sum(query[1], query[2]));
            }
        }
    }
}

namespace AtCoder
{
#pragma warning disable CA1815 // Override equals and operator equals on value types
    public interface INumOperator<T> : IEqualityComparer<T>, IComparer<T> where T : struct
    {
        /// <summary>
        /// MinValue
        /// </summary>
        public T MinValue { get; }
        /// <summary>
        /// MaxValue
        /// </summary>
        public T MaxValue { get; }
        /// <summary>
        /// Addition operator +
        /// </summary>
        /// <returns><paramref name="x"/> + <paramref name="y"/></returns>
        T Add(T x, T y);
        /// <summary>
        /// Subtraction operator -
        /// </summary>
        /// <returns><paramref name="x"/> - <paramref name="y"/></returns>
        T Subtract(T x, T y);
        /// <summary>
        /// Multiplication operator *
        /// </summary>
        /// <returns><paramref name="x"/> * <paramref name="y"/></returns>
        T Multiply(T x, T y);
        /// <summary>
        /// Division operator /
        /// </summary>
        /// <returns><paramref name="x"/> / <paramref name="y"/></returns>
        T Divide(T x, T y);
        /// <summary>
        /// Remainder operator %
        /// </summary>
        /// <returns><paramref name="x"/> % <paramref name="y"/></returns>
        T Modulo(T x, T y);
        /// <summary>
        /// Greater than operator &gt;
        /// </summary>
        /// <returns><paramref name="x"/> &gt; <paramref name="y"/></returns>
        bool GreaterThan(T x, T y);
        /// <summary>
        /// Greater than or equal operator &gt;=
        /// </summary>
        /// <returns><paramref name="x"/> &gt;= <paramref name="y"/></returns>
        bool GreaterThanOrEqual(T x, T y);
        /// <summary>
        /// Less than operator &lt;
        /// </summary>
        /// <returns><paramref name="x"/> &lt; <paramref name="y"/></returns>
        bool LessThan(T x, T y);
        /// <summary>
        /// Less than or equal operator &lt;=
        /// </summary>
        /// <returns><paramref name="x"/> &lt;= <paramref name="y"/></returns>
        bool LessThanOrEqual(T x, T y);
    }
    public readonly struct IntOperator : INumOperator<int>
    {
        public int MinValue => int.MinValue;
        public int MaxValue => int.MaxValue;
        public int Add(int x, int y) => x + y;
        public int Subtract(int x, int y) => x - y;
        public int Multiply(int x, int y) => x * y;
        public int Divide(int x, int y) => x / y;
        public int Modulo(int x, int y) => x % y;
        public bool GreaterThan(int x, int y) => x > y;
        public bool GreaterThanOrEqual(int x, int y) => x >= y;
        public bool LessThan(int x, int y) => x < y;
        public bool LessThanOrEqual(int x, int y) => x <= y;
        public int Compare(int x, int y) => x.CompareTo(y);
        public bool Equals(int x, int y) => x == y;
        public int GetHashCode(int obj) => obj.GetHashCode();
    }
    public readonly struct LongOperator : INumOperator<long>
    {
        public long MinValue => long.MinValue;
        public long MaxValue => long.MaxValue;
        public long Add(long x, long y) => x + y;
        public long Subtract(long x, long y) => x - y;
        public long Multiply(long x, long y) => x * y;
        public long Divide(long x, long y) => x / y;
        public long Modulo(long x, long y) => x % y;
        public bool GreaterThan(long x, long y) => x > y;
        public bool GreaterThanOrEqual(long x, long y) => x >= y;
        public bool LessThan(long x, long y) => x < y;
        public bool LessThanOrEqual(long x, long y) => x <= y;
        public int Compare(long x, long y) => x.CompareTo(y);
        public bool Equals(long x, long y) => x == y;
        public int GetHashCode(long obj) => obj.GetHashCode();
    }
    public readonly struct UIntOperator : INumOperator<uint>
    {
        public uint MinValue => uint.MinValue;
        public uint MaxValue => uint.MaxValue;
        public uint Add(uint x, uint y) => x + y;
        public uint Subtract(uint x, uint y) => x - y;
        public uint Multiply(uint x, uint y) => x * y;
        public uint Divide(uint x, uint y) => x / y;
        public uint Modulo(uint x, uint y) => x % y;
        public bool GreaterThan(uint x, uint y) => x > y;
        public bool GreaterThanOrEqual(uint x, uint y) => x >= y;
        public bool LessThan(uint x, uint y) => x < y;
        public bool LessThanOrEqual(uint x, uint y) => x <= y;
        public int Compare(uint x, uint y) => x.CompareTo(y);
        public bool Equals(uint x, uint y) => x == y;
        public int GetHashCode(uint obj) => obj.GetHashCode();
    }
    public readonly struct ULongOperator : INumOperator<ulong>
    {
        public ulong MinValue => ulong.MinValue;
        public ulong MaxValue => ulong.MaxValue;
        public ulong Add(ulong x, ulong y) => x + y;
        public ulong Subtract(ulong x, ulong y) => x - y;
        public ulong Multiply(ulong x, ulong y) => x * y;
        public ulong Divide(ulong x, ulong y) => x / y;
        public ulong Modulo(ulong x, ulong y) => x % y;
        public bool GreaterThan(ulong x, ulong y) => x > y;
        public bool GreaterThanOrEqual(ulong x, ulong y) => x >= y;
        public bool LessThan(ulong x, ulong y) => x < y;
        public bool LessThanOrEqual(ulong x, ulong y) => x <= y;
        public int Compare(ulong x, ulong y) => x.CompareTo(y);
        public bool Equals(ulong x, ulong y) => x == y;
        public int GetHashCode(ulong obj) => obj.GetHashCode();
    }
    public readonly struct DoubleOperator : INumOperator<double>
    {
        public double MinValue => double.MinValue;
        public double MaxValue => double.MaxValue;
        public double Add(double x, double y) => x + y;
        public double Subtract(double x, double y) => x - y;
        public double Multiply(double x, double y) => x * y;
        public double Divide(double x, double y) => x / y;
        public double Modulo(double x, double y) => x % y;
        public bool GreaterThan(double x, double y) => x > y;
        public bool GreaterThanOrEqual(double x, double y) => x >= y;
        public bool LessThan(double x, double y) => x < y;
        public bool LessThanOrEqual(double x, double y) => x <= y;
        public int Compare(double x, double y) => x.CompareTo(y);
        public bool Equals(double x, double y) => x == y;
        public int GetHashCode(double obj) => obj.GetHashCode();
    }
#pragma warning restore CA1815 // Override equals and operator equals on value types
}

#region AtCoderLibrary

namespace AtCoder
{

    /// <summary>
    /// 長さ N の配列に対し、
    /// <list type="bullet">
    /// <item>
    /// <description>要素の 1 点変更</description>
    /// </item>
    /// <item>
    /// <description>区間の要素の総和</description>
    /// </item>
    /// </list>
    /// <para>を O(log⁡N) で求めることが出来るデータ構造です。</para>
    /// </summary>
    public class IntFenwickTree : FenwickTree<int, IntOperator> { public IntFenwickTree(int n) : base(n) { } }

    /// <summary>
    /// 長さ N の配列に対し、
    /// <list type="bullet">
    /// <item>
    /// <description>要素の 1 点変更</description>
    /// </item>
    /// <item>
    /// <description>区間の要素の総和</description>
    /// </item>
    /// </list>
    /// <para>を O(log⁡N) で求めることが出来るデータ構造です。</para>
    /// </summary>
    public class UIntFenwickTree : FenwickTree<uint, UIntOperator> { public UIntFenwickTree(int n) : base(n) { } }

    /// <summary>
    /// 長さ N の配列に対し、
    /// <list type="bullet">
    /// <item>
    /// <description>要素の 1 点変更</description>
    /// </item>
    /// <item>
    /// <description>区間の要素の総和</description>
    /// </item>
    /// </list>
    /// <para>を O(log⁡N) で求めることが出来るデータ構造です。</para>
    /// </summary>
    public class LongFenwickTree : FenwickTree<long, LongOperator> { public LongFenwickTree(int n) : base(n) { } }

    /// <summary>
    /// 長さ N の配列に対し、
    /// <list type="bullet">
    /// <item>
    /// <description>要素の 1 点変更</description>
    /// </item>
    /// <item>
    /// <description>区間の要素の総和</description>
    /// </item>
    /// </list>
    /// <para>を O(log⁡N) で求めることが出来るデータ構造です。</para>
    /// </summary>
    public class ULongFenwickTree : FenwickTree<ulong, ULongOperator> { public ULongFenwickTree(int n) : base(n) { } }

    /// <summary>
    /// 長さ N の配列に対し、
    /// <list type="bullet">
    /// <item>
    /// <description>要素の 1 点変更</description>
    /// </item>
    /// <item>
    /// <description>区間の要素の総和</description>
    /// </item>
    /// </list>
    /// <para>を O(log⁡N) で求めることが出来るデータ構造です。</para>
    /// </summary>
    // TODO: public class ModIntFenwickTree : FenwickTree<ModInt, ModIntOperator> { public ModIntFenwickTree(int n) : base(n) { } }


    /// <summary>
    /// 長さ N の配列に対し、
    /// <list type="bullet">
    /// <item>
    /// <description>要素の 1 点変更</description>
    /// </item>
    /// <item>
    /// <description>区間の要素の総和</description>
    /// </item>
    /// </list>
    /// <para>を O(log⁡N) で求めることが出来るデータ構造です。</para>
    /// </summary>
    /// <typeparam name="TValue">配列要素の型</typeparam>
    /// <typeparam name="TOp">配列要素の操作を表す型</typeparam>
    [DebuggerTypeProxy(typeof(FenwickTree<,>.DebugView))]
    public class FenwickTree<TValue, TOp>
        where TValue : struct
        where TOp : struct, INumOperator<TValue>
    {
        private static readonly TOp op = default;
        private readonly TValue[] data;

        /// <summary>
        /// 長さ <paramref name="n"/> の配列aを持つ <see cref="FenwickTree{TValue, TOp}"/> クラスの新しいインスタンスを作ります。
        /// </summary>
        /// <remarks>
        /// <para>制約: 0≤<paramref name="n"/>≤10^8</para>
        /// <para>計算量: O(<paramref name="n"/>)</para>
        /// </remarks>
        /// <param name="n">配列の長さ</param>
        public FenwickTree(int n)
        {
            Debug.Assert(unchecked((uint)n <= 100_000_000));
            data = new TValue[n + 1];
        }

        /// <summary>
        /// a[<paramref name="p"/>] += <paramref name="x"/> を行います。
        /// </summary>
        /// <remarks>
        /// <para>制約: 0≤<paramref name="p"/>&lt;n</para>
        /// <para>計算量: O(log n)</para>
        /// </remarks>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Add(int p, TValue x)
        {
            Debug.Assert(unchecked((uint)p < data.Length));
            for (p++; p < data.Length; p += InternalBit.ExtractLowestSetBit(p))
            {
                data[p] = op.Add(data[p], x);
            }
        }

        /// <summary>
        /// a[<paramref name="l"/>] + a[<paramref name="l"/> - 1] + ... + a[<paramref name="r"/> - 1] を返します。
        /// </summary>
        /// <remarks>
        /// <para>制約: 0≤<paramref name="l"/>≤<paramref name="r"/>≤n</para>
        /// <para>計算量: O(log n)</para>
        /// </remarks>
        /// <returns>a[<paramref name="l"/>] + a[<paramref name="l"/> - 1] + ... + a[<paramref name="r"/> - 1]</returns>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public TValue Sum(int l, int r)
        {
            Debug.Assert(0 <= l && l <= r && r < data.Length);
            return op.Subtract(Sum(r), Sum(l));
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        private TValue Sum(int r)
        {
            TValue s = default;
            for (; r > 0; r -= InternalBit.ExtractLowestSetBit(r))
            {
                s = op.Add(s, data[r]);
            }
            return s;
        }


        [DebuggerDisplay("Value = {" + nameof(value) + "}, Sum = {" + nameof(sum) + "}")]
        private struct DebugItem
        {
            public DebugItem(TValue value, TValue sum)
            {
                this.sum = sum;
                this.value = value;
            }
            [DebuggerBrowsable(DebuggerBrowsableState.Never)]
            public readonly TValue value;
            [DebuggerBrowsable(DebuggerBrowsableState.Never)]
            public readonly TValue sum;
        }
        private class DebugView
        {
            private readonly FenwickTree<TValue, TOp> fenwickTree;
            public DebugView(FenwickTree<TValue, TOp> fenwickTree)
            {
                this.fenwickTree = fenwickTree;
            }
            [DebuggerBrowsable(DebuggerBrowsableState.RootHidden)]
            public DebugItem[] Items
            {
                get
                {
                    var data = fenwickTree.data;
                    var items = new DebugItem[data.Length - 1];
                    items[0] = new DebugItem(data[1], data[1]);
                    for (int i = 2; i < data.Length; i++)
                    {
                        int length = InternalBit.ExtractLowestSetBit(i);
                        var pr = i - length - 1;
                        var sum = op.Add(data[i], 0 <= pr ? items[pr].sum : default);
                        var val = op.Subtract(sum, items[i - 2].sum);
                        items[i - 1] = new DebugItem(val, sum);
                    }
                    return items;
                }
            }
        }
    }
}
namespace AtCoder.Internal
{
    public static class InternalBit
    {
        /// <summary>
        /// _blsi_u32 OR <paramref name="n"/> &amp; -<paramref name="n"/>
        /// <para><paramref name="n"/>で立っているうちの最下位の 1 ビットのみを立てた整数を返す</para>
        /// </summary>
        /// <param name="n"></param>
        /// <returns><paramref name="n"/> &amp; -<paramref name="n"/></returns>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static int ExtractLowestSetBit(int n)
        {
            if (Bmi1.IsSupported)
            {
                return (int)Bmi1.ExtractLowestSetBit((uint)n);
            }
            return n & -n;
        }
    }
}
#endregion AtCoderLibrary