Problem:
Score : 600 points

Problem Statement

You are given an integer sequence of length N, a = {a_1, a_2, …, a_N}, and an integer K.

a has N(N+1)/2 non-empty contiguous subsequences, {a_l, a_{l+1}, …, a_r} (1 ≤ l ≤ r ≤ N). Among them, how many have an arithmetic mean that is greater than or equal to K?

Constraints

All input values are integers.

1 ≤ N ≤ 2 \times 10^5

1 ≤ K ≤ 10^9

1 ≤ a_i ≤ 10^9

Input

Input is given from Standard Input in the following format:

N K
a_1
a_2
:
a_N

Output

Print the number of the non-empty contiguous subsequences with an arithmetic mean that is greater than or equal to K.

Sample Input 1

3 6
7
5
7

Sample Output 1

5

All the non-empty contiguous subsequences of a are listed below:

{a_1} = {7}

{a_1, a_2} = {7, 5}

{a_1, a_2, a_3} = {7, 5, 7}

{a_2} = {5}

{a_2, a_3} = {5, 7}

{a_3} = {7}

Their means are 7, 6, 19/3, 5, 6 and 7, respectively, and five among them are 6 or greater. Note that {a_1} and {a_3} are indistinguishable by the values of their elements, but we count them individually.

Sample Input 2

1 2
1

Sample Output 2

0

Sample Input 3

7 26
10
20
30
40
30
20
10

Sample Output 3

13

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Linq;

using E = System.Linq.Enumerable;

internal partial class Solver {
    public void Run() {
        var n = ni();
        var k = ni();
        var a = ni(n);
        for (int i = 0; i < n; i++) {
            a[i] -= k;
        }
        var s = new long[n + 1];
        for (int i = 1; i <= n; i++) {
            s[i] += s[i - 1] + a[i - 1];
        }

        var d = IndexDictionaryFactory.Create(s);
        var bit = new BinaryIndexTree(n + 2);
        long ans = 0;
        for (int i = 0; i <= n; i++) {
            var index = d.GetIndex(s[i]);
            var lowerNum = bit.Sum(0, index + 1);
            ans += lowerNum;
            bit.Add(index, 1);
        }
        cout.WriteLine(ans);
    }

}
public class BinaryIndexTree {
    private readonly long[] array;
    public BinaryIndexTree(int size) {
        array = new long[size];
    }
    public long Sum(int begin, int end) {
        if (begin != 0) {
            return Sum(0, end) - Sum(0, begin);
        }

        long val = 0;
        end--;
        for (; end >= 0; end = (end & (end + 1)) - 1) {
            val += array[end];
        }

        return val;
    }

    public void Add(int k, long val) {
        for (; k < array.Length; k |= k + 1) {
            array[k] += val;
        }
    }

    /// <summary>return min pos where sum(A[0] .. A[pos]) >= w</summary>
    public int LowerBound(long w) {
        if (w <= 0) {
            return 0;
        }

        int x = 0, k = 1, N = array.Length;
        while ((k << 1) <= N) {
            k <<= 1;
        }

        for (; k > 0; k >>= 1) {
            if (x + k - 1 < N && array[x + k - 1] < w) {
                w -= array[x + k - 1];
                x += k;
            }
        }
        return (x == N) ? -1 : x;
    }
}

public class IndexDictionary<T> {
    private readonly Dictionary<T, int> _toIndex;
    private readonly T[] _array;

    public IndexDictionary(IEnumerable<T> source) : this(source, Comparer<T>.Default) { }

    public IndexDictionary(IEnumerable<T> source, IComparer<T> comparer) {
        _array = source.Distinct().ToArray();
        Array.Sort(_array, comparer);
        _toIndex = new Dictionary<T, int>(_array.Length);
        int index = -1;
        foreach (var x in _array) {
            _toIndex[x] = ++index;
        }
    }

    public int Count { get { return _array.Length; } }

    public T this[int index] { get { return _array[index]; } }

    public int GetIndex(T value) { return _toIndex[value]; }
}

public class IndexDictionaryFactory {
    public static IndexDictionary<T> Create<T>(IEnumerable<T> source) {
        return new IndexDictionary<T>(source);
    }
}

// PREWRITEN CODE BEGINS FROM HERE
internal partial class Solver : Scanner {
    public static void Main(string[] args) {
#if LOCAL
        byte[] inputBuffer = new byte[1000000];
        var inputStream = Console.OpenStandardInput(inputBuffer.Length);
        Console.SetIn(new StreamReader(inputStream, Console.InputEncoding, false, inputBuffer.Length));
        new Solver(Console.In, Console.Out).Run();
#else
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        new Solver(Console.In, Console.Out).Run();
        Console.Out.Flush();
#endif
    }

#pragma warning disable IDE0052
    private readonly TextReader cin;
    private readonly TextWriter cout;
#pragma warning restore IDE0052

    public Solver(TextReader reader, TextWriter writer)
        : base(reader) {
        cin = reader;
        cout = writer;
    }
    public Solver(string input, TextWriter writer)
        : this(new StringReader(input), writer) {
    }

#pragma warning disable IDE1006
#pragma warning disable IDE0051
    private int ni() { return NextInt(); }
    private int[] ni(int n) { return NextIntArray(n); }
    private long nl() { return NextLong(); }
    private long[] nl(int n) { return NextLongArray(n); }
    private double nd() { return NextDouble(); }
    private double[] nd(int n) { return NextDoubleArray(n); }
    private string ns() { return Next(); }
    private string[] ns(int n) { return NextArray(n); }
#pragma warning restore IDE1006
#pragma warning restore IDE0051
}

internal static class LinqPadExtension {
    public static T Dump<T>(this T obj) {
#if LOCAL
        return LINQPad.Extensions.Dump(obj);
#else
        return obj;
#endif
    }
}

public class Scanner {
    private readonly TextReader Reader;
    private readonly Queue<string> TokenQueue = new Queue<string>();
    private readonly CultureInfo ci = CultureInfo.InvariantCulture;

    public Scanner()
        : this(Console.In) {
    }

    public Scanner(TextReader reader) {
        Reader = reader;
    }

    public int NextInt() { return int.Parse(Next(), ci); }
    public long NextLong() { return long.Parse(Next(), ci); }
    public double NextDouble() { return double.Parse(Next(), ci); }
    public string[] NextArray(int size) {
        string[] array = new string[size];
        for (int i = 0; i < size; i++) {
            array[i] = Next();
        }

        return array;
    }
    public int[] NextIntArray(int size) {
        int[] array = new int[size];
        for (int i = 0; i < size; i++) {
            array[i] = NextInt();
        }

        return array;
    }

    public long[] NextLongArray(int size) {
        long[] array = new long[size];
        for (int i = 0; i < size; i++) {
            array[i] = NextLong();
        }

        return array;
    }

    public double[] NextDoubleArray(int size) {
        double[] array = new double[size];
        for (int i = 0; i < size; i++) {
            array[i] = NextDouble();
        }

        return array;
    }

    public string Next() {
        if (TokenQueue.Count == 0) {
            if (!StockTokens()) {
                throw new InvalidOperationException();
            }
        }
        return TokenQueue.Dequeue();
    }

    public bool HasNext() {
        if (TokenQueue.Count > 0) {
            return true;
        }

        return StockTokens();
    }

    private static readonly char[] _separator = new[] { ' ', '\t' };
    private bool StockTokens() {
        while (true) {
            string line = Reader.ReadLine();
            if (line == null) {
                return false;
            }

            string[] tokens = line.Split(_separator, StringSplitOptions.RemoveEmptyEntries);
            if (tokens.Length == 0) {
                continue;
            }

            foreach (string token in tokens) {
                TokenQueue.Enqueue(token);
            }

            return true;
        }
    }
}