#region いつもの
using AtCoder;
using AtCoder.Internal;
using AtCoderProject;
using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Numerics;
using System.Runtime.CompilerServices;
using System.Runtime.Intrinsics.X86;
using static AtCoderProject.Global;
using BigInteger = System.Numerics.BigInteger;
using BitOperations = System.Numerics.BitOperations;
using IEnumerable = System.Collections.IEnumerable;
using IEnumerator = System.Collections.IEnumerator;
using StringBuilder = System.Text.StringBuilder;
using Unsafe = System.Runtime.CompilerServices.Unsafe;

namespace AtCoderProject
{
    using System.IO;
    using System.Text;
    using System.Diagnostics;
    using System.Runtime.CompilerServices;
    using System.Linq.Expressions;

    public static class Global
    {
        public static int Gcd(params int[] nums)
        {
            var gcd = nums[0];
            for (var i = 1; i < nums.Length; i++)
                gcd = Gcd(nums[i], gcd);
            return gcd;
        }
        public static int Gcd(int a, int b) => b > a ? Gcd(b, a) : (b == 0 ? a : Gcd(b, a % b));
        public static int Lcm(int a, int b) => a / Gcd(a, b) * b;
        public static int Lcm(params int[] nums)
        {
            var lcm = nums[0];
            for (var i = 1; i < nums.Length; i++)
                lcm = Lcm(lcm, nums[i]);
            return lcm;
        }
        public static long Gcd(params long[] nums)
        {
            var gcd = nums[0];
            for (var i = 1; i < nums.Length; i++)
                gcd = Gcd(nums[i], gcd);
            return gcd;
        }
        public static long Gcd(long a, long b) => b > a ? Gcd(b, a) : (b == 0 ? a : Gcd(b, a % b));
        public static long Lcm(long a, long b) => a / Gcd(a, b) * b;

        public static long Lcm(params long[] nums)
        {
            var lcm = nums[0];
            for (var i = 1; i < nums.Length; i++)
                lcm = Lcm(lcm, nums[i]);
            return lcm;
        }

        public static T[] NewArray<T>(int len0, T value) => new T[len0].Fill(value);
        public static T[] NewArray<T>(int len0, Func<T> factory)
        {
            var arr = new T[len0];
            for (int i = 0; i < arr.Length; i++) arr[i] = factory();
            return arr;
        }
        public static T[][] NewArray<T>(int len0, int len1, T value) where T : struct
        {
            var arr = new T[len0][];
            for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, value);
            return arr;
        }
        public static T[][] NewArray<T>(int len0, int len1, Func<T> factory)
        {
            var arr = new T[len0][];
            for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, factory);
            return arr;
        }
        public static T[][][] NewArray<T>(int len0, int len1, int len2, T value) where T : struct
        {
            var arr = new T[len0][][];
            for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, value);
            return arr;
        }
        public static T[][][] NewArray<T>(int len0, int len1, int len2, Func<T> factory)
        {
            var arr = new T[len0][][];
            for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, factory);
            return arr;
        }
        public static T[][][][] NewArray<T>(int len0, int len1, int len2, int len3, T value) where T : struct
        {
            var arr = new T[len0][][][];
            for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, len3, value);
            return arr;
        }
        public static T[][][][] NewArray<T>(int len0, int len1, int len2, int len3, Func<T> factory)
        {
            var arr = new T[len0][][][];
            for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, len3, factory);
            return arr;
        }


        public static long Pow(long x, int y)
        {
            long res = 1;
            for (; y > 0; y >>= 1)
            {
                if ((y & 1) == 1) res *= x;
                x *= x;
            }
            return res;
        }
        public static BigInteger ParseBigInteger(ReadOnlySpan<char> s)
        {
            /* 自前実装の方が速い */
            if (s[0] == '-') return -ParseBigInteger(s[1..]);
            BigInteger res;
            if (s.Length % 9 == 0)
                res = 0;
            else
            {
                res = new BigInteger(int.Parse(s.Slice(0, s.Length % 9)));
                s = s.Slice(s.Length % 9);
            }

            while (s.Length > 0)
            {
                var sp = s.Slice(0, 9);
                res *= 1000_000_000;
                res += int.Parse(sp);
                s = s.Slice(9);
            }
            return res;
        }
        public static int PopCount(int x) => BitOperations.PopCount((uint)x);
        public static int PopCount(long x) => BitOperations.PopCount((ulong)x);
        public static int PopCount(ulong x) => BitOperations.PopCount(x);
        public static int MSB(int x) => BitOperations.Log2((uint)x);
        public static int MSB(uint x) => BitOperations.Log2(x);
        public static int MSB(long x) => BitOperations.Log2((ulong)x);
        public static int MSB(ulong x) => BitOperations.Log2(x);
        public static int LSB(int x) => BitOperations.TrailingZeroCount((uint)x);
        public static int LSB(uint x) => BitOperations.TrailingZeroCount(x);
        public static int LSB(long x) => BitOperations.TrailingZeroCount((ulong)x);
        public static int LSB(ulong x) => BitOperations.TrailingZeroCount(x);

    }
    public static class Ext
    {

        public static bool UpdateMax<T>(this ref T r, T val) where T : struct, IComparable<T>
        {
            if (r.CompareTo(val) < 0) { r = val; return true; }
            return false;
        }
        public static bool UpdateMin<T>(this ref T r, T val) where T : struct, IComparable<T>
        {
            if (r.CompareTo(val) > 0) { r = val; return true; }
            return false;
        }
        public static T[] Fill<T>(this T[] arr, T value)
        {
            Array.Fill(arr, value);
            return arr;
        }
        public static T[] Sort<T>(this T[] arr) { Array.Sort(arr); return arr; }
        public static string[] Sort(this string[] arr) => Sort(arr, StringComparer.Ordinal);
        public static T[] Sort<T, U>(this T[] arr, Expression<Func<T, U>> selector) where U : IComparable<U> => Sort(arr, ExComparer<T>.CreateExp(selector));
        public static T[] Sort<T>(this T[] arr, Comparison<T> comparison) { Array.Sort(arr, comparison); return arr; }
        public static T[] Sort<T>(this T[] arr, IComparer<T> comparer) { Array.Sort(arr, comparer); return arr; }
        public static T[] Reverse<T>(this T[] arr) { Array.Reverse(arr); return arr; }
        public static (int index, T max) MaxBy<T>(this T[] arr) where T : IComparable<T>
        {
            T max = arr[0];
            int maxIndex = 0;
            for (int i = 0; i < arr.Length; i++)
            {
                if (max.CompareTo(arr[i]) < 0)
                {
                    max = arr[i];
                    maxIndex = i;
                }
            }
            return (maxIndex, max);
        }
        public static (int index, T max) MaxBy<T, TMax>(this T[] arr, Func<T, TMax> maxBySelector) where TMax : IComparable<TMax>
        {
            var maxItem = maxBySelector(arr[0]);
            var max = arr[0];
            int maxIndex = 0;
            for (int i = 0; i < arr.Length; i++)
            {
                var nx = maxBySelector(arr[i]);
                if (maxItem.CompareTo(nx) < 0)
                {
                    maxItem = nx;
                    max = arr[i];
                    maxIndex = i;
                }
            }
            return (maxIndex, max);
        }
        public static (TSource item, TMax max) MaxBy<TSource, TMax>
            (this IEnumerable<TSource> source, Func<TSource, TMax> maxBySelector)
            where TMax : IComparable<TMax>
        {
            TMax max;
            TSource maxByItem;
            var e = source.GetEnumerator();
            e.MoveNext();
            maxByItem = e.Current;
            max = maxBySelector(maxByItem);
            while (e.MoveNext())
            {
                var item = e.Current;
                var next = maxBySelector(item);
                if (max.CompareTo(next) < 0)
                {
                    max = next;
                    maxByItem = item;
                }
            }
            return (maxByItem, max);
        }
        public static (int index, T min) MinBy<T>(this T[] arr) where T : IComparable<T>
        {
            T min = arr[0];
            int minIndex = 0;
            for (int i = 0; i < arr.Length; i++)
            {
                if (min.CompareTo(arr[i]) > 0)
                {
                    min = arr[i];
                    minIndex = i;
                }
            }
            return (minIndex, min);
        }
        public static (int index, T min) MinBy<T, TMin>(this T[] arr, Func<T, TMin> minBySelector) where TMin : IComparable<TMin>
        {
            var minItem = minBySelector(arr[0]);
            var min = arr[0];
            int minIndex = 0;
            for (int i = 0; i < arr.Length; i++)
            {
                var nx = minBySelector(arr[i]);
                if (minItem.CompareTo(nx) > 0)
                {
                    minItem = nx;
                    min = arr[i];
                    minIndex = i;
                }
            }
            return (minIndex, min);
        }
        public static (TSource item, TMin min) MinBy<TSource, TMin>
            (this IEnumerable<TSource> source, Func<TSource, TMin> minBySelector)
            where TMin : IComparable<TMin>
        {
            TMin min;
            TSource minByItem;

            var e = source.GetEnumerator();
            e.MoveNext();
            minByItem = e.Current;
            min = minBySelector(minByItem);
            while (e.MoveNext())
            {
                var item = e.Current;
                var next = minBySelector(item);
                if (min.CompareTo(next) > 0)
                {
                    min = next;
                    minByItem = item;
                }
            }
            return (minByItem, min);
        }
        public static Dictionary<TKey, int> GroupCount<TSource, TKey>(this IEnumerable<TSource> source, Func<TSource, TKey> keySelector) => source.GroupBy(keySelector).ToDictionary(g => g.Key, g => g.Count());
        public static Dictionary<TKey, int> GroupCount<TKey>(this IEnumerable<TKey> source) => source.GroupCount(i => i);
        public static Span<T> AsSpan<T>(this List<T> list, int start = 0) => Unsafe.As<Tuple<T[]>>(list).Item1.AsSpan(start, list.Count);
        public static ref T Get<T>(this T[] arr, int index)
        {
            if (index < 0)
                return ref arr[arr.Length + index];
            return ref arr[index];
        }
        public static TValue Get<TKey, TValue>(this IDictionary<TKey, TValue> dic, TKey key)
        {
            dic.TryGetValue(key, out var v);
            return v;
        }
    }
    public static class ExComparer<T>
    {
        class ExpressionComparer<K> : IComparer<T> where K : IComparable<K>
        {
            private class ParameterReplaceVisitor : ExpressionVisitor
            {
                private readonly ParameterExpression from;
                private readonly ParameterExpression to;
                public ParameterReplaceVisitor(ParameterExpression from, ParameterExpression to)
                {
                    this.from = from;
                    this.to = to;
                }
                protected override Expression VisitParameter(ParameterExpression node) => node == from ? to : base.VisitParameter(node);
            }

            readonly Comparison<T> func;
            public ExpressionComparer(Expression<Func<T, K>> expression)
            {
                var paramA = expression.Parameters[0];
                var paramB = Expression.Parameter(typeof(T));
                var f2 = (Expression<Func<T, K>>)new ParameterReplaceVisitor(expression.Parameters[0], paramB).Visit(expression);
                var compExp = Expression.Lambda<Comparison<T>>(Expression.Call(
                        expression.Body,
                        typeof(K).GetMethod(nameof(IComparable<K>.CompareTo), new[] { typeof(K) }),
                        f2.Body),
                        paramA, paramB);
                this.func = compExp.Compile();
            }
            public int Compare(T x, T y) => func(x, y);
            public override bool Equals(object obj) => obj is ExpressionComparer<K> c && this.func == c.func;
            public override int GetHashCode() => func.GetHashCode();
        }
        class ReverseComparer : IComparer<T>
        {
            private static Comparer<T> orig = Comparer<T>.Default;
            public int Compare(T y, T x) => orig.Compare(x, y);
            public override bool Equals(object obj) => obj is ReverseComparer;
            public override int GetHashCode() => GetType().GetHashCode();
        }
        public static IComparer<T> CreateExp<K>(Expression<Func<T, K>> expression) where K : IComparable<K> => new ExpressionComparer<K>(expression);
        public static readonly IComparer<T> DefaultReverse = new ReverseComparer();
    }
    public class ΔDebugView<T> { private IEnumerable<T> collection; public ΔDebugView(IEnumerable<T> collection) { this.collection = collection ?? throw new ArgumentNullException(nameof(collection)); }[DebuggerBrowsable(DebuggerBrowsableState.RootHidden)] public T[] Items => collection.ToArray(); }


    [DebuggerStepThrough]
    public class ConsoleReader
    {
        const int BufSize = 1 << 12;
        private readonly byte[] buffer = new byte[BufSize];
        private readonly Stream input;
        private readonly Encoding encoding;
        private int pos = 0;
        private int len = 0;
        public ConsoleReader(Stream input, Encoding encoding) { this.input = input; this.encoding = encoding; }
        public ConsoleReader() : this(Console.OpenStandardInput(), Console.InputEncoding) { }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        private void MoveNext() { if (++pos >= len) { len = input.Read(buffer, 0, buffer.Length); if (len == 0) { buffer[0] = 10; } pos = 0; } }

        public int Int
        {
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            get
            {
                int res = 0;
                bool neg = false;
                while (buffer[pos] < 48) { neg = buffer[pos] == 45; MoveNext(); }
                do { res = checked(res * 10 + (buffer[pos] ^ 48)); MoveNext(); } while (48 <= buffer[pos]);
                return neg ? -res : res;
            }
        }
        public int Int0 => this.Int - 1;
        public long Long
        {
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            get
            {
                long res = 0;
                bool neg = false;
                while (buffer[pos] < 48) { neg = buffer[pos] == 45; MoveNext(); }
                do { res = res * 10 + (buffer[pos] ^ 48); MoveNext(); } while (48 <= buffer[pos]);
                return neg ? -res : res;
            }
        }
        public long Long0 => this.Long - 1;
        public string String
        {
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            get
            {
                var sb = new List<byte>();
                while (buffer[pos] <= 32) MoveNext();
                do { sb.Add(buffer[pos]); MoveNext(); } while (32 < buffer[pos]);
                return this.encoding.GetString(sb.ToArray());
            }
        }
        public string Ascii
        {
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            get
            {
                var sb = new StringBuilder();
                while (buffer[pos] <= 32) MoveNext();
                do { sb.Append((char)buffer[pos]); MoveNext(); } while (32 < buffer[pos]);
                return sb.ToString();
            }
        }
        public string Line
        {
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            get
            {
                var sb = new List<byte>();
                while (buffer[pos] <= 32) MoveNext();
                do { sb.Add(buffer[pos]); MoveNext(); } while (buffer[pos] != 10 && buffer[pos] != 13);
                return this.encoding.GetString(sb.ToArray());
            }
        }
        public char Char
        {
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            get
            {
                while (buffer[pos] <= 32) MoveNext();
                char res = (char)buffer[pos];
                MoveNext();
                return res;
            }
        }
        public double Double => double.Parse(this.Ascii);

        [DebuggerStepThrough]
        public struct RepeatReader
        {
            ConsoleReader cr;
            int count;
            public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; }
            public T[] Select<T>(Func<ConsoleReader, T> factory) { var arr = new T[count]; for (var i = 0; i < count; i++) arr[i] = factory(cr); return arr; }
            public T[] Select<T>(Func<ConsoleReader, int, T> factory) { var arr = new T[count]; for (var i = 0; i < count; i++) arr[i] = factory(cr, i); return arr; }
            public string[] Line { get { var arr = new string[count]; for (var i = 0; i < count; i++) arr[i] = cr.Line; return arr; } }
            public string[] String { get { var arr = new string[count]; for (var i = 0; i < count; i++) arr[i] = cr.String; return arr; } }
            public string[] Ascii { get { var arr = new string[count]; for (var i = 0; i < count; i++) arr[i] = cr.Ascii; return arr; } }
            public int[] Int { get { var arr = new int[count]; for (var i = 0; i < count; i++) arr[i] = cr.Int; return arr; } }
            public int[] Int0 { get { var arr = new int[count]; for (var i = 0; i < count; i++) arr[i] = cr.Int0; return arr; } }
            public long[] Long { get { var arr = new long[count]; for (var i = 0; i < count; i++) arr[i] = cr.Long; return arr; } }
            public long[] Long0 { get { var arr = new long[count]; for (var i = 0; i < count; i++) arr[i] = cr.Long0; return arr; } }
            public double[] Double { get { var arr = new double[count]; for (var i = 0; i < count; i++) arr[i] = cr.Double; return arr; } }

            public static implicit operator int[](RepeatReader rr) => rr.Int;
            public static implicit operator long[](RepeatReader rr) => rr.Long;
            public static implicit operator double[](RepeatReader rr) => rr.Double;
            public static implicit operator string[](RepeatReader rr) => rr.Ascii;
        }
        public RepeatReader Repeat(int count) => new RepeatReader(this, count);

        [DebuggerStepThrough]
        public struct SplitReader
        {
            ConsoleReader cr;
            public SplitReader(ConsoleReader cr) { this.cr = cr; }
            public string[] String { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<string>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.String); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } }
            public string[] Ascii { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<string>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Ascii); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } }
            public int[] Int { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<int>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Int); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } }
            public int[] Int0 { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<int>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Int0); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } }
            public long[] Long { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<long>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Long); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } }
            public long[] Long0 { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<long>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Long0); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } }
            public double[] Double { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<double>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Double); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } }

            public static implicit operator int[](SplitReader sr) => sr.Int;
            public static implicit operator long[](SplitReader sr) => sr.Long;
            public static implicit operator double[](SplitReader sr) => sr.Double;
            public static implicit operator string[](SplitReader sr) => sr.Ascii;
        }
        public SplitReader Split => new SplitReader(this);

        public static implicit operator int(ConsoleReader cr) => cr.Int;
        public static implicit operator long(ConsoleReader cr) => cr.Long;
        public static implicit operator double(ConsoleReader cr) => cr.Double;
        public static implicit operator string(ConsoleReader cr) => cr.Ascii;
    }
    [DebuggerStepThrough]
    public class ConsoleWriter
    {
        [DebuggerBrowsable(DebuggerBrowsableState.Never)] public readonly StreamWriter sw;
        public ConsoleWriter() : this(Console.OpenStandardOutput(), Console.OutputEncoding) { }
        public ConsoleWriter(Stream output, Encoding encoding) { sw = new StreamWriter(output, encoding); }
        public void Flush() => sw.Flush();
        public ConsoleWriter WriteLine(ReadOnlySpan<char> obj) { sw.WriteLine(obj); return this; }
        public ConsoleWriter WriteLine<T>(T obj) { sw.WriteLine(obj.ToString()); return this; }
        public ConsoleWriter WriteLineJoin<T>(Span<T> col) => WriteMany(' ', (ReadOnlySpan<T>)col);
        public ConsoleWriter WriteLineJoin<T>(ReadOnlySpan<T> col) => WriteMany(' ', col);
        public ConsoleWriter WriteLineJoin<T>(IEnumerable<T> col) => WriteMany(' ', col);
        public ConsoleWriter WriteLineJoin<T>(params T[] col) => WriteMany(' ', col);
        public ConsoleWriter WriteLineJoin(params object[] col) => WriteMany(' ', col);
        public ConsoleWriter WriteLineJoin<T1, T2>(T1 v1, T2 v2)
        {
            sw.Write(v1.ToString()); sw.Write(' ');
            sw.WriteLine(v2.ToString()); return this;
        }
        public ConsoleWriter WriteLineJoin<T1, T2, T3>(T1 v1, T2 v2, T3 v3)
        {
            sw.Write(v1.ToString()); sw.Write(' ');
            sw.Write(v2.ToString()); sw.Write(' ');
            sw.WriteLine(v3.ToString()); return this;
        }
        public ConsoleWriter WriteLineJoin<T1, T2, T3, T4>(T1 v1, T2 v2, T3 v3, T4 v4)
        {
            sw.Write(v1.ToString()); sw.Write(' ');
            sw.Write(v2.ToString()); sw.Write(' ');
            sw.Write(v3.ToString()); sw.Write(' ');
            sw.WriteLine(v4.ToString()); return this;
        }
        public ConsoleWriter WriteLines<T>(Span<T> col) => WriteMany('\n', (ReadOnlySpan<T>)col);
        public ConsoleWriter WriteLines<T>(ReadOnlySpan<T> col) => WriteMany('\n', col);
        public ConsoleWriter WriteLines<T>(IEnumerable<T> col) => WriteMany('\n', col);
        public ConsoleWriter WriteLineGrid<T>(IEnumerable<IEnumerable<T>> cols)
        {
            foreach (var col in cols)
                WriteLineJoin(col);
            return this;
        }
        private ConsoleWriter WriteMany<T>(char sep, ReadOnlySpan<T> col)
        {
            var en = col.GetEnumerator();
            if (!en.MoveNext())
                return this;
            sw.Write(en.Current.ToString());
            while (en.MoveNext())
            {
                sw.Write(sep);
                sw.Write(en.Current.ToString());
            }
            sw.WriteLine();
            return this;
        }
        private ConsoleWriter WriteMany<T>(char sep, IEnumerable<T> col)
        {
            var en = col.GetEnumerator();
            if (!en.MoveNext())
                return this;
            sw.Write(en.Current.ToString());
            while (en.MoveNext())
            {
                sw.Write(sep);
                sw.Write(en.Current.ToString());
            }
            sw.WriteLine();
            return this;
        }
    }
}
public partial class Program
{
    [System.Diagnostics.DebuggerBrowsable(System.Diagnostics.DebuggerBrowsableState.Never)] public ConsoleReader cr;
    [System.Diagnostics.DebuggerBrowsable(System.Diagnostics.DebuggerBrowsableState.Never)] public ConsoleWriter cw;
    public Program(ConsoleReader reader, ConsoleWriter writer) { this.cr = reader; this.cw = writer; System.Globalization.CultureInfo.CurrentCulture = System.Globalization.CultureInfo.InvariantCulture; }
    static void Main() => new Program(new ConsoleReader(), new ConsoleWriter()).Run();
    public void Run()
    {
        var res = Calc();
        if (res is double)
            cw.WriteLine(Result((double)res));
        else if (res is bool)
            cw.WriteLine(Result((bool)res));
        else if (res != null)
            cw.WriteLine(res.ToString());
        cw.Flush();
    }
}
public partial class Program
{
    public static string Result(double d) => d.ToString("0.####################", System.Globalization.CultureInfo.InvariantCulture);
    #endregion
    public static string Result(bool b) => b ? "Yes" : "No";
    private object Calc()
    {
        int n = cr, q = cr;

        var fw = new LongFenwickTree(n);
        int[] a = cr.Repeat(n);
        for (int i = 0; i < a.Length; i++)
        {
            fw.Add(i, a[i]);
        }

        for (int i = 0; i < q; i++)
        {
            if (cr.Int == 0)
            {
                fw.Add(cr.Int, cr.Int);
            }
            else
            {
                cw.WriteLine(fw.Sum(cr.Int, cr.Int));
            }
        }
        return null;
    }
}

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

Measured memory_bytes: 44700