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.BufferedReader;
import java.io.File;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

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

public class Main {

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

	BufferedReader in;
	PrintWriter out;
	StringTokenizer st = new StringTokenizer("");

	private void run() throws IOException {
		if (new File("input.txt").exists())
			in = new BufferedReader(new FileReader("input.txt"));
		else
			in = new BufferedReader(new InputStreamReader(System.in));
		if (new File("output.txt").exists())
			out = new PrintWriter("output.txt");
		else
			out = new PrintWriter(System.out);

		solve();

		in.close();
		out.close();
	}

	final int maxn = 22;
	final int p = 1000 * 1000 * 1000 + 7;

	int n;
	long s;
	long f[] = new long[maxn];
	long ans;

	long inv[] = new long[maxn];
	long finv[] = new long[maxn];

	TreeMap<Long, Long> polynom = new TreeMap<>();

	void rec(int index, long a, long pow) {
		if (index == n) {
			if (polynom.containsKey(pow))
				polynom.put(pow, (polynom.get(pow) + a) % p);
			else
				polynom.put(pow, a);
		} else {
			rec(index + 1, a, pow);
			rec(index + 1, (p - a) % p, pow + f[index] + 1);
		}
	}

	long getC(long n, int m) {
		n %= p;
		long c = 1;
		for (long i = n - m + 1; i <= n; i++)
			c = (c * i) % p;
		c = (c * finv[m]) % p;
		return c;
	}

	void precalc() {
		inv[1] = 1;
		for (int i = 2; i < maxn; i++)
			inv[i] = (p - ((p / i) * inv[p % i]) % p) % p;
		finv[0] = 1;
		for (int i = 1; i < maxn; i++)
			finv[i] = (finv[i - 1] * inv[i]) % p;
	}

	void solve() throws IOException {
		precalc();
		n = nextInt();
		s = nextLong();
		for (int i = 0; i < n; i++)
			f[i] = nextLong();

		rec(0, 1, 0);
		ans = 0;
		for (long pow : polynom.keySet()) {
			long k = s - pow;
			if (k >= 0) {
				long c = getC(n + k - 1, n - 1);
				// System.err.println(k + " " + c);
				ans = (ans + c * polynom.get(pow)) % p;
			}
		}

		out.println(ans);
	}

	String nextLine() throws IOException {
		st = new StringTokenizer("");
		return in.readLine();
	}

	String nextToken() throws IOException {
		while (!st.hasMoreTokens()) {
			st = new StringTokenizer(in.readLine());
		}
		return st.nextToken();
	}

	int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

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

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

	boolean EOF() throws IOException {
		while (!st.hasMoreTokens()) {
			String str = in.readLine();
			if (str == null)
				return true;
			st = new StringTokenizer(str);
		}
		return false;
	}

}