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

import static java.lang.Math.*;
import static java.util.Arrays.*;
import static java.util.Collections.*;

public class Main{
	
	// ArrayList<Integer> lis = new ArrayList<Integer>();
	// ArrayList<String> lis = new ArrayList<String>();
	//  PriorityQueue<P> que = new PriorityQueue<P>();
	// PriorityQueue<Integer> que = new PriorityQueue<Integer>();
	//  Stack<Integer> que = new Stack<Integer>();
    //	static long sum=0;
	// 1000000007 (10^9+7)
	static int mod = 1000000007;
	//static int mod = 1000000009,r=0; ArrayList<Integer> l[]= new ArrayList[n];
   // static int dx[]={1,-1,0,0};
//	static int dy[]={0,0,1,-1};
//	static int dx[]={1,-1,0,0,1,1,-1,-1};
//  static int dy[]={0,0,1,-1,1,-1,1,-1};
	//static Set<Integer> set = new HashSet<Integer>();p
	
public  static void main(String[] args)   throws Exception, IOException{
   //String line=""; throws Exception, IOException
   //(line=br.readLine())!=null
	//Scanner sc =new Scanner(System.in);
	// !!caution!! int long //  
	Reader sc = new Reader(System.in);


 //,a=sc.nextInt(),b=sc.nextInt();
 	 int n=sc.nextInt();
    long f[]=new long[n],s=sc.nextLong()+n-1;
     
	for (int i = 0; i <n ; i++){
		f[i]=sc.nextLong();
	}

	long a[]=new long [2];
	long d[]=new long[22];
      d[0]++;

	for (int i = 1; i <=20 ; i++){
		d[i]=exGCD(i, mod)[1];d[i]+=mod; d[i]%=mod;
		d[i]*=d[i-1];
        d[i]%=mod;
	}
	
	//db(d);
	
	long r=0;
	
	for(int i=0,c=1;i<1<<n;i++){
	  long 	x=s,k=0;
	    for(int t=0;t<n;t++){
	    	if( bit(i,t) ){ k++;  x-=f[t]+1;      }
	    }
	   if( k%2==0 )c=1 ; else c=-1;
	   if(x<0)continue; 
	    x%=mod;
	  r+=c*com( x,n-1,d[n-1] );
	  r+=mod;
	  r%=mod;
	 // db(i,x,r);
	}
	
	
	System.out.println(r);

}

static boolean bit(int x,int k){
	// weather k-th bit (from right) be one or zero
	return  ( 0 < ( (x>>k) & 1 )  )  ? true:false;
}
   
static long com( long n, int m ,long d) {//beware n<m�I
	
	if( n<m )return 0;
		
  long r=1;
	 for(int i=0;i<m;i++){
		 r*=n--; r%=mod;
	 }

	 r*=d; r%=mod;
	return r;
}

 static long[] exGCD(long a, long b)
{
	if(a == 0 || b == 0)return null;
	int as = Long.signum(a);
	int bs = Long.signum(b);
	a = Math.abs(a); b = Math.abs(b);
	long p = 1, q = 0, r = 0, s = 1;
	while(b > 0){
		long c = a / b;
		long d;
		d = a; a = b; b = d % b;
		d = p; p = q; q = d - c * q;
		d = r; r = s; s = d - c * s;
	}
	// can be minus! 
	return new long[]{a, p * as, r * bs};
}

static void db(Object... os){
    System.err.println(Arrays.deepToString(os));

}

}


  /* 
   * class P implements Comparable<P>{
//		implements Comparable<Pair>
		int id; long d;
		P(int id,long d){
			this.id=id;
			this.d=d;
		} 
		public int compareTo(P x){
		   	 return  0<=d-x.d?1:-1 ;  //ascend
		   }
	 
 }



class Pair implements Comparable<Pair>{
//	implements Comparable<Pair>
	int a,b;
	Pair(int a,int b){
		this.a=a;
		this.b=b;
	} 
	public int compareTo(Pair x){
	   	 return a-x.a; //descend
	   }
}*/

class Reader
{ 
	private BufferedReader x;
	private StringTokenizer st;
	
	public Reader(InputStream in)
	{
		x = new BufferedReader(new InputStreamReader(in));
		st = null;
	}
	public String nextString() throws IOException
	{
		while( st==null || !st.hasMoreTokens() )
			st = new StringTokenizer(x.readLine());
		return st.nextToken();
	}
	public int nextInt() throws IOException
	{
		return Integer.parseInt(nextString());
	}
	public long nextLong() throws IOException
	{
		return Long.parseLong(nextString());
	}
	public double nextDouble() throws IOException
	{
		return Double.parseDouble(nextString());
	}
}