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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.NoSuchElementException;


public class Main{
	static FastScanner sc = new FastScanner();
	static PrintWriter out = new PrintWriter(System.out);
	//static String S;
	//static String T;
	static int n;
	static long dp [][];
	//static boolean flag [][];
	static long a [];
	static final int mod = 1_000_000_007;
	//static LinkedList <Integer> adj []; 
	
	public static void main(String[] args) {
		n = sc.nextInt();
		int K = sc.nextInt();
		a = sc.nextLongArray(n, true);
		dp = new long [n+1][K+1];
		
		dp[0][0] = 1;
		long add [] = new long [K+2];
		
		for (int i=1; i<=n; i++) {
			add[0]=0;
			
			for (int j=1; j<=K+1; j++)
				add[j] = (add[j-1]+dp[i-1][j-1])%mod;
			
			for (int j=0; j<=K; j++)
				dp[i][j] = (add[j+1]-add[(int)Math.max(0, j-a[i])]+mod)%mod;
			
		}
		out.println(dp[n][K]);
		
		out.flush();
	}
	
		static class FastScanner {
		    private final InputStream in = System.in;
		    private final byte[] buffer = new byte[1024];
		    private int ptr = 0;
		    private int buflen = 0;

		    private boolean hasNextByte() {
		      if (ptr < buflen) {
		        return true;
		      } else {
		        ptr = 0;
		        try {
		          buflen = in.read(buffer);
		        } catch (IOException e) {
		          e.printStackTrace();
		        }
		        if (buflen <= 0) {
		          return false;
		        }
		      }
		      return true;
		    }

		    private int readByte() {
		      if (hasNextByte()) return buffer[ptr++];
		      else return -1;
		    }

		    private static boolean isPrintableChar(int c) {
		      return 33 <= c && c <= 126;
		    }

		    private void skipUnprintable() {
		      while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
		    }

		    public boolean hasNext() {
		      skipUnprintable();
		      return hasNextByte();
		    }

		    public String next() {
		      if (!hasNext()) throw new NoSuchElementException();
		      StringBuilder sb = new StringBuilder();
		      int b = readByte();
		      while (isPrintableChar(b)) {
		        sb.appendCodePoint(b);
		        b = readByte();
		      }
		      return sb.toString();
		    }

		    public long nextLong() {
		      if (!hasNext()) throw new NoSuchElementException();
		      long n = 0;
		      boolean minus = false;
		      int b = readByte();
		      if (b == '-') {
		        minus = true;
		        b = readByte();
		      }
		      if (b < '0' || '9' < b) {
		        throw new NumberFormatException();
		      }
		      while (true) {
		        if ('0' <= b && b <= '9') {
		          n *= 10;
		          n += b - '0';
		        } else if (b == -1 || !isPrintableChar(b)) {
		          return minus ? -n : n;
		        } else {
		          throw new NumberFormatException();
		        }
		        b = readByte();
		      }
		    }

		    public int nextInt() {
		      return (int) nextLong();
		    }
		    
		    public double nextDouble(){
		    	return Double.parseDouble(next());
		    }

		    public int[] nextIntArray(int N, boolean oneBased) {
		      if (oneBased) {
		        int[] array = new int[N + 1];
		        for (int i = 1; i <= N; i++) {
		          array[i] = sc.nextInt();
		        }
		        return array;
		      } else {
		        int[] array = new int[N];
		        for (int i = 0; i < N; i++) {
		          array[i] = sc.nextInt();
		        }
		        return array;
		      }
		    }

		    public long[] nextLongArray(int N, boolean oneBased) {
		      if (oneBased) {
		        long[] array = new long[N + 1];
		        for (int i = 1; i <= N; i++) {
		          array[i] = sc.nextLong();
		        }
		        return array;
		      } else {
		        long[] array = new long[N];
		        for (int i = 0; i < N; i++) {
		          array[i] = sc.nextLong();
		        }
		        return array;
		      }
		    }
		  }

		}