Problem:
Score : 100 points

Problem Statement

There are N children, numbered 1, 2, \ldots, N.

They have decided to share K candies among themselves.
Here, for each i (1 \leq i \leq N), Child i must receive between 0 and a_i candies (inclusive).
Also, no candies should be left over.

Find the number of ways for them to share candies, modulo 10^9 + 7.
Here, two ways are said to be different when there exists a child who receives a different number of candies.

Constraints

All values in input are integers.

1 \leq N \leq 100

0 \leq K \leq 10^5

0 \leq a_i \leq K

Input

Input is given from Standard Input in the following format:

N K
a_1 a_2 \ldots a_N

Output

Print the number of ways for the children to share candies, modulo 10^9 + 7.

Sample Input 1

3 4
1 2 3

Sample Output 1

5

There are five ways for the children to share candies, as follows:

(0, 1, 3)

(0, 2, 2)

(1, 0, 3)

(1, 1, 2)

(1, 2, 1)

Here, in each sequence, the i-th element represents the number of candies that Child i receives.

Sample Input 2

1 10
9

Sample Output 2

0

There may be no ways for the children to share candies.

Sample Input 3

2 0
0 0

Sample Output 3

1

There is one way for the children to share candies, as follows:

(0, 0)

Sample Input 4

4 100000
100000 100000 100000 100000

Sample Output 4

665683269

Be sure to print the answer modulo 10^9 + 7.

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

#if DEBUG
using Microsoft.VisualStudio.TestTools.UnitTesting;
#endif

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Contest
{
    class Program
    {
        static void Main(string[] args)
        {
            var scanner = new IO.StreamScanner(Console.OpenStandardInput());

            var n = scanner.Integer();
            var k = scanner.Integer();
            var a = scanner.ScanLine().Split().Select(v => long.Parse(v)).ToList();

            var ans = GetAns(n, k, a);
            IO.Printer.Out.WriteLine(ans);
            IO.Printer.Out.Flush();
        }

        static long mod = 1000000007;
        public static long GetAns(int n, int k, List<long> a)
        {
            if (k == 0) return 1;
            var dp = new long[k + 1];
            for (int j = 0; j <= a[n - 1]; j++) dp[j] = 1;

            for (int i = n - 2; i >= 0; i--)
            {
                var accum = GetAccum(dp);
                var newDp = new long[k + 1];
                for (int j = 0; j < k + 1; j++)
                {
                    newDp[j] += accum[j];
                    if (j - a[i] - 1 >= 0)
                        newDp[j] -= accum[j - a[i] - 1];
                    newDp[j] += mod;
                    newDp[j] %= mod;
                }
                dp = newDp;
            }
            return dp[k];
        }

        public static long[] GetAccum(long[] arr)
        {
            var ret = new long[arr.Length];
            ret[0] = arr[0];
            for (int i = 1; i < arr.Length; i++)
            {
                ret[i] = ret[i - 1] + arr[i];
                ret[i] %= mod;
            }

            return ret;
        }
    }

#if DEBUG

    [TestClass]
    public class Test
    {
        [TestMethod]
        public void Test1()
        {
            var n = 3;
            var k = 4;
            var a = new List<long> { 1, 2, 3 };
            var exp = 5l;
            var ans = Program.GetAns(n, k, a);
            Assert.AreEqual(exp, ans);
        }

        [TestMethod]
        public void Test2()
        {
            var n = 1;
            var k = 10;
            var a = new List<long> { 0 };
            var exp = 0l;
            var ans = Program.GetAns(n, k, a);
            Assert.AreEqual(exp, ans);
        }

        [TestMethod]
        public void Test3()
        {
            var n = 2;
            var k = 0;
            var a = new List<long> { 0, 0 };
            var exp = 1l;
            var ans = Program.GetAns(n, k, a);
            Assert.AreEqual(exp, ans);
        }

        [TestMethod]
        public void Test4()
        {
            var n = 4;
            var k = 100000;
            var a = new List<long> { 100000, 100000, 100000, 100000 };
            var exp = 665683269L;
            var ans = Program.GetAns(n, k, a);
            Assert.AreEqual(exp, ans);
        }
    }

#endif
}

namespace IO
{
    using System.IO;
    using System.Text;
    using System.Globalization;

    public class Printer : StreamWriter
    {
        static Printer()
        {
            Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false };
        }

        public static Printer Out { get; set; }

        public override IFormatProvider FormatProvider
        {
            get { return CultureInfo.InvariantCulture; }
        }

        public Printer(Stream stream)
            : base(stream, new UTF8Encoding(false, true))
        {
        }

        public Printer(Stream stream, Encoding encoding)
            : base(stream, encoding)
        {
        }

        public void Write<T>(string format, T[] source)
        {
            base.Write(format, source.OfType<object>().ToArray());
        }

        public void WriteLine<T>(string format, T[] source)
        {
            base.WriteLine(format, source.OfType<object>().ToArray());
        }
    }

    public class StreamScanner
    {
        public StreamScanner(Stream stream)
        {
            str = stream;
        }

        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof;

        public bool IsEndOfStream
        {
            get { return isEof; }
        }

        private byte read()
        {
            if (isEof) return 0;
            if (ptr < len) return buf[ptr++];
            ptr = 0;
            if ((len = str.Read(buf, 0, 1024)) > 0) return buf[ptr++];
            isEof = true;
            return 0;
        }

        public char Char()
        {
            byte b;
            do b = read(); while ((b < 33 || 126 < b) && !isEof);
            return (char)b;
        }

        public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }

        public string ScanLine()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b != '\n'; b = (char)read())
                if (b == 0) break;
                else if (b != '\r') sb.Append(b);
            return sb.ToString();
        }

        public long Long()
        {
            if (isEof) return long.MinValue;
            long ret = 0;
            byte b;
            var ng = false;
            do b = read(); while (b != 0 && b != '-' && (b < '0' || '9' < b));
            if (b == 0) return long.MinValue;
            if (b == '-')
            {
                ng = true;
                b = read();
            }
            for (; ; b = read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                ret = ret * 10 + b - '0';
            }
        }

        public int Integer()
        {
            return (isEof) ? int.MinValue : (int)Long();
        }

        public double Double()
        {
            var s = Scan();
            return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN;
        }

        static T[] enumerate<T>(int n, Func<T> f)
        {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f();
            return a;
        }

        public char[] Char(int n)
        {
            return enumerate(n, Char);
        }

        public string[] Scan(int n)
        {
            return enumerate(n, Scan);
        }

        public double[] Double(int n)
        {
            return enumerate(n, Double);
        }

        public int[] Integer(int n)
        {
            return enumerate(n, Integer);
        }

        public long[] Long(int n)
        {
            return enumerate(n, Long);
        }
    }
}