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.

Examples

Input

3 4
1 2 3


Output

5


Input

1 10
9


Output

0


Input

2 0
0 0


Output

1


Input

4 100000
100000 100000 100000 100000


Output

665683269

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

public class Main{

	
	static int MOD=(int)1e9+7;
	
	public static void main(String[] args) throws IOException {
		Scanner sc=new Scanner();
		PrintWriter out=new PrintWriter(System.out);
		int n=sc.nextInt(),k=sc.nextInt();
		int []a=new int [n];
		for(int i=0;i<n;i++)
			a[i]=sc.nextInt();
		int [][]dp=new int [n+1][k+1],pre=new int [n+1][k+1];
		pre[n][k]=dp[n][k]=1;
		for(int idx=n-1;idx>=0;idx--) {
			int sum=0;
			for(int eaten=0;eaten<=k;eaten++)
			{
				int ans=pre[idx+1][Math.min(k, eaten+a[idx])];
				if(eaten>0) {
					ans=ans-pre[idx+1][eaten-1];
					if(ans<0)
						ans+=MOD;
				}
				dp[idx][eaten]=ans;
				sum=sum+ans;
				if(sum>=MOD)
					sum-=MOD;
				pre[idx][eaten]=sum;
			}
		}
		out.println(dp[0][0]);
		out.close();
	}
	
	static class Scanner
	{
		BufferedReader br;
		StringTokenizer st;
		Scanner(){
			br=new BufferedReader(new InputStreamReader(System.in));
		}
		Scanner(String fileName) throws FileNotFoundException{
			br=new BufferedReader(new FileReader(fileName));
		}
		String next() throws IOException {
			while(st==null || !st.hasMoreTokens())
				st=new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		String nextLine() throws IOException {
			return br.readLine();
		}
		int nextInt() throws IOException{
			return Integer.parseInt(next());
		}
		long nextLong()  throws NumberFormatException, IOException {
			return Long.parseLong(next());
		}
		double nextDouble() throws NumberFormatException, IOException {
			return Double.parseDouble(next());
		}
	}
}
