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.lang.*;
import static java.lang.Math.*;
import java.lang.reflect.*;
import java.math.BigInteger;
import static java.math.BigInteger.*;
import java.security.CodeSource;
import java.security.KeyStore;
import java.util.*;
import static java.util.Arrays.*;
import java.util.jar.JarEntry;
import java.util.jar.JarFile;
import java.util.logging.Level;
import java.util.logging.Logger;

// https://netbeans.org/kb/73/java/editor-codereference_ru.html#display

public class Main {
    
    final long mod = (long)1e9 + 7;
    int n;
    long s;
    long[] f;
    long[] invFact = new long[1000];
    {
        invFact[0] = 1;
        long f = 1;
        for (int i = 1; i < invFact.length; i++) {
            f = (f * i) % mod;
            invFact[i] = valueOf(f).modInverse(valueOf(mod)).longValue();
        }
    }
    
    long C( int l, long b ){
        long ans = 1;
        for( long x = b-l+1; x <= b; ++x ){
            ans = (x%mod * ans) % mod;
        }
        ans = (ans * invFact[l]) % mod;
        return ans;
    }

    void solve(){
        for( int n = 0; n <= 10; ++n ){
            for (int m = 0; m <= n; m++) {
                err.print( " " + C(m,n) );
            }
            err.println();
        }
        
        n = sc.nextInt();
        s = sc.nextLong();
        f = new long[n];
        for (int i = 0; i < f.length; i++) {
            f[i] = sc.nextLong();
        }
        
        long ans = 0;
        for (int msk = 0; msk < (1<<n); msk++) {
            long curS = s;
            for (int i = 0; i < n; i++) {
                if( ((msk>>i)&1) == 1 ){
                    curS -= f[i] + 1;
                }
            }
            if( 0 <= curS ){
                long comb = C(n-1, curS+n-1);
                //err.println( msk +") "+ comb );
                if( Integer.bitCount(msk) % 2 == 0 )
                    ans = (ans + comb) % mod;
                else
                    ans = (ans - comb + mod) % mod;
            }
        }
        ans = (ans%mod + mod) % mod;
        out.println(ans);
    }

    
    
    
    
    //------------------------------------------------------------------//
    
    private void run(){
        err = System.err;
        boolean oj = true;
        try {
            oj = System.getProperty("MYLOCAL") == null;
        } catch (Exception e) {
        }
        
        if( oj ){
            sc = new FastScanner(new InputStreamReader(System.in));
            out = new PrintWriter(new OutputStreamWriter(System.out));
        }
        else{
            try {
                sc = new FastScanner(new FileReader("input.txt"));
                out = new PrintWriter(new FileWriter("output.txt"));
            } catch ( IOException e) {
                MLE();
            }
        }
        solve();
        
        out.flush();
    }
    
    FastScanner sc;
    PrintWriter out;
    PrintStream err;
    
    
    void MLE(){
        int[][] arr = new int[1024*1024][];
        for (int i = 0; i < arr.length; i++) {
            arr[i] = new int[1024*1024];
        }
    }


    class FastScanner {

        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStreamReader reader) {
            br = new BufferedReader(reader);
            st = new StringTokenizer("");
        }

        String next() {
            while( !st.hasMoreElements() )
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException ex) {
                    MLE();
                }
            return st.nextToken();
        }
        
        int nextInt(){ return Integer.parseInt(next());}

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

    public static void main(String[] args){
        new Main().run();
    }

}