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: Wrong Answer)

import java.io.*; 
import java.util.*; 

public class Main{ 
	
	static class FastReader{ 
		BufferedReader br; 
		StringTokenizer st; 

		public FastReader() 
		{ 
			br = new BufferedReader(new
					InputStreamReader(System.in)); 
		} 

		String next() 
		{ 
			while (st == null || !st.hasMoreElements()) 
			{ 
				try
				{ 
					st = new StringTokenizer(br.readLine()); 
				} 
				catch (IOException e) 
				{ 
					e.printStackTrace(); 
				} 
			} 
			return st.nextToken(); 
		} 

		int nextInt() 
		{ 
			return Integer.parseInt(next()); 
		} 

		long nextLong() 
		{ 
			return Long.parseLong(next()); 
		} 

		double nextDouble() 
		{ 
			return Double.parseDouble(next()); 
		} 

		String nextLine() 
		{ 
			String str = ""; 
			try
			{ 
				str = br.readLine(); 
			} 
			catch (IOException e) 
			{ 
				e.printStackTrace(); 
			} 
			return str; 
		} 
	}

	public static void main(String[] args) 
	{ 
        FastReader sc = new FastReader(); 
        //PrintWriter out = new PrintWriter(System.out); 

        int n = sc.nextInt();
        int k = sc.nextInt();
        long mod = 1000000007L;
        long[] arr = new long[n+1];
        long[][] dp = new long[n+1][k+1];

        for(int i=0;i<n;i++){
        	arr[i] = sc.nextLong();
        }

        for(int i=0;i<=k;i++)
        	dp[0][i] = 1;
        
        for(int i=0;i<n;i++){
        	for(int j=0;j<=k;j++){
        		if(j>=arr[i]+1)
        			dp[i+1][j] = ( dp[i+1][j] + dp[i][j]- dp[i][j-(int)arr[i]-1] )%mod;
        		else
        			dp[i+1][j] = ( dp[i+1][j] + dp[i][j] )%mod;
        	}

        	if(i+1!=n)
		    	for(int j=1;j<=k;j++){
		    		dp[i+1][j] = ( dp[i+1][j] + dp[i+1][j-1] )%mod;
		    	}
        }

        // for(int i=0;i<=n;i++){
        // 	for(int j=0;j<=k;j++){
        // 		//System.out.print(dp[i][j]+" ");
        // 	}
        // 	//System.out.println("\n-------"+dp[i][0]+"---------   "+dp[i][k]);
        // }

        System.out.println( dp[n][k] );
	}
}