Problem: Devu wants to decorate his garden with flowers. He has purchased n boxes, where the i-th box contains fi flowers. All flowers in a single box are of the same color (hence they are indistinguishable). Also, no two boxes have flowers of the same color.

Now Devu wants to select exactly s flowers from the boxes to decorate his garden. Devu would like to know, in how many different ways can he select the flowers from each box? Since this number may be very large, he asks you to find the number modulo (109 + 7). 

Devu considers two ways different if there is at least one box from which different number of flowers are selected in these two ways.

Input

The first line of input contains two space-separated integers n and s (1 ≤ n ≤ 20, 0 ≤ s ≤ 1014).

The second line contains n space-separated integers f1, f2, ... fn (0 ≤ fi ≤ 1012).

Output

Output a single integer — the number of ways in which Devu can select the flowers modulo (109 + 7).

Examples

Input

2 3
1 3


Output

2


Input

2 4
2 2


Output

1


Input

3 5
1 3 2


Output

3

Note

Sample 1. There are two ways of selecting 3 flowers: {1, 2} and {0, 3}.

Sample 2. There is only one way of selecting 4 flowers: {2, 2}.

Sample 3. There are three ways of selecting 5 flowers: {1, 2, 2}, {0, 3, 2}, and {1, 3, 1}.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.math.*;
import java.util.concurrent.*;

public final class devu_and_flowers
{
    static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	static FastScanner sc=new FastScanner(br);
    static PrintWriter out=new PrintWriter(System.out);
	static Random rnd=new Random();
	static long mod=(long)(1e9+7);
	
	static long C(long n,long diff)
	{
		long ret=1,upper=n+diff-1;
		
		for(long x=upper;x>diff;x--)
		{
			long now=x%mod;
				
			ret=(ret*now)%mod;
		}
		
		return (ret*pow(fact(n-1),mod-2))%mod;
	}
	
	static long fact(long n)
	{
		long ret=1;
		
		for(long i=1;i<=n;i++)	
		{
			ret=(ret*i)%mod;
		}
		
		return ret;
	}
	
	static long pow(long a,long b)
	{
		long x=1,y=a;
		
		while(b>0)
		{
			if(b%2==1)
			{
				x=(x*y)%mod;
			}
			
			y=(y*y)%mod;b=b/2;
		}
		
		return x;
	}
	
	static Map<Long,Long> merge(Map<Long,Long> m1,long now)
	{	
		Map<Long,Long> m2=new HashMap<>(),ret=new HashMap<>();
		
		m2.put(0L,1L);m2.put(now,(-1L+mod)%mod);
		
		for(Map.Entry<Long,Long> en1:m1.entrySet())
		{
			for(Map.Entry<Long,Long> en2:m2.entrySet())
			{
				long add=en1.getKey()+en2.getKey(),mul=(en1.getValue()*en2.getValue())%mod;
				
				ret.put(add,(ret.getOrDefault(add,0L)+mul)%mod);
			}
		}
		
		return ret;
	}
	
    public static void main(String args[]) throws Exception
    {
		int n=sc.nextInt();long s=sc.nextLong();
		
		long[] a=new long[n];
		
		for(int i=0;i<n;i++)
		{
			a[i]=sc.nextLong();
		}
		
		// 1-x^a[i]+1..
		
		Map<Long,Long> m1=new HashMap<>();m1.put(0L,1L);
		
		for(int i=0;i<n;i++)
		{
			m1=merge(m1,a[i]+1);
		}
		
		long res=0;
		
		for(Map.Entry<Long,Long> en:m1.entrySet())
		{	
			long curr=en.getKey();
			
			if(curr<=s)
			{
				long diff=s-curr;
				
				long now=C(n,diff);
			
				long mul=(en.getValue()*now)%mod;
				
				res=(res+mul)%mod;
			}
		}
		
		out.println(res);out.close();
    }
	
	private static class Pair
	{
		long pow,cof;
		
		public Pair(long pow,long cof)
		{
			this.pow=pow;this.cof=cof;
		}
	}
}
class FastScanner
{
    BufferedReader in;
    StringTokenizer st;

    public FastScanner(BufferedReader in) {
        this.in = in;
    }
	
    public String nextToken() throws Exception {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }
	
	public String next() throws Exception {
		return nextToken().toString();
	}
	
    public int nextInt() throws Exception {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws Exception {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws Exception {
        return Double.parseDouble(nextToken());
    }
}