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.PrintWriter;
import java.util.Scanner;

public class E451 {

	static class Solver {

		int N;
		long S, MOD = 1_000_000_007, cookie;
		long[] boxes;

		long modPow(long k, long exp) {
			if (exp == 0)
				return 1;
			if (exp == 1)
				return k;
			long hs = (k * k) % MOD;
			if ((exp & 1) == 1)
				return (k * modPow(hs, exp / 2)) % MOD;
			return modPow(hs, exp / 2) % MOD;
		}

		long modInv(long k) {
			return modPow(k, MOD - 2);
		}

		void bakeACookie() {
			long h = 1;
			for (int i = 2; i < N; i++) {
				h *= i;
				h %= MOD;
			}
			cookie = modInv(h);
		}

		long chooseMod(long n, long k) {
			if (n < k)
				return 0;
			if (n == k)
				return 1;
			long top = 1;
			for (int i = 0; i < k; i++) {
				top *= (n - i) % MOD;
				top %= MOD;
			}
			// if (Math.random() < 0.00001)
			// System.out.println(n + " " + k + " --> " + top + ", " + modInv(k) + " --> " +
			// ((top * modInv(k)) % MOD));
			return (top * cookie) % MOD;

		}

		// @SuppressWarnings("unchecked")
		public void solve(int testNumber, Scanner s, PrintWriter out) {

			N = s.nextInt();
			bakeACookie();
			S = s.nextLong();
			boxes = new long[N];
			for (int i = 0; i < N; i++)
				boxes[i] = s.nextLong();

			long ways = 0;
			for (int i = 0; i < 1 << N; i++) {
				// overcounting on bits
				long over = 0;
				for (int c = 0; c < N; c++) {
					if ((i & (1 << c)) > 0)
						over += boxes[c] + 1;
				}
				if ((Integer.bitCount(i) & 1) == 1)
					ways -= chooseMod(S - over + N - 1, N - 1);
				else
					ways += chooseMod(S - over + N - 1, N - 1);
				// if (Math.random() < 0.0001)
				// out.printf("%d choose %d = %d\n", S - over + N - 1, N - 1, chooseMod(S - over
				// + N - 1, N - 1));

			}

			out.println(Math.floorMod(ways, MOD));

		}

	}

	public static void main(String[] args) {

//		 Scanner s = new Scanner("2 3\n" + "1 3\n");
//		 Scanner s = new Scanner("2 4\n" + "2 2\n");
//		 Scanner s = new Scanner("3 5\n" + "1 3 2\n");
//		Scanner s = new Scanner("20 4385085334307\n"
//				+ "273634411136 208521328637 450482376435 844118010709 197241285878 472126475472 2414038897 672334205413 809269727018 409013884362 739986692075 953956651947 462216461906 388007176838 245504550965 527140291750 632844435887 550532123833 757200390348 944901802640\n");
		 Scanner s = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);

		Solver solver = new Solver();
		solver.solve(1, s, out);

		out.close();
		s.close();

	}
}