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.List;
import java.io.InputStreamReader;
import java.io.IOException;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.ArrayList;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Reader;
import java.io.Writer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Niyaz Nigmatullin
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		FastScanner in = new FastScanner(inputStream);
		FastPrinter out = new FastPrinter(outputStream);
		TaskE solver = new TaskE();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskE {

    static final int MOD = 1000000007;

    static int mul(int a, int b) {
        return (int) ((long) a * b % MOD);
    }

    static int[] REV;
    static {
        REV = new int[25];
        for (int i = 1; i < REV.length; i++) {
            REV[i] = MathUtils.modPow(i, MOD - 2, MOD);
        }
    }

    static int f(long n_, int k) {
        --k;
        n_ += k;
        if (k > n_ || k < 0 || n_ < 0) return 0;
        int ans = 1;
        int n = (int) (n_ % MOD + MOD);
        for (int i = 0; i < k; i++) {
            ans = mul(ans, (n - i));
            ans = mul(ans, REV[i + 1]);
        }
        return ans;
    }

    public void solve(int testNumber, FastScanner in, FastPrinter out) {
        int n = in.nextInt();
        long s = in.nextLong();
        long[] f = new long[n];
        for (int i = 0; i < n; i++) {
            f[i] = in.nextLong();
        }
        int ans = 0;
        for (int mask = 0; mask < 1 << n; mask++) {
            long cs = 0;
            for (int i = 0; i < n; i++) {
                if (((mask >> i) & 1) == 1) {
                    cs += f[i] + 1;
                }
            }
            if (cs > s) {
                continue;
            }
            if ((Integer.bitCount(mask) & 1) == 1) {
                ans -= f(s - cs, n);
                if (ans < 0) ans += MOD;
            } else {
                ans += f(s - cs, n);
                if (ans >= MOD) ans -= MOD;
            }
        }
        out.println(ans);
    }
}

class MathUtils {


    public static int modPow(int a, int b, int mod) {
        int ret = 1;
        a = (a % mod + mod) % mod;
        while (b > 0) {
            if ((b & 1) == 1) {
                ret = (int) ((long) ret * a % mod);
            }
            a = (int) ((long) a * a % mod);
            b >>= 1;
        }
        return ret;
    }

    }

class FastScanner extends BufferedReader {

    public FastScanner(InputStream is) {
        super(new InputStreamReader(is));
    }

    public int read() {
        try {
            int ret = super.read();
//            if (isEOF && ret < 0) {
//                throw new InputMismatchException();
//            }
//            isEOF = ret == -1;
            return ret;
        } catch (IOException e) {
            throw new InputMismatchException();
        }
    }

    public String next() {
        StringBuilder sb = new StringBuilder();
        int c = read();
        while (isWhiteSpace(c)) {
            c = read();
        }
        if (c < 0) {
            return null;
        }
        while (c >= 0 && !isWhiteSpace(c)) {
            sb.appendCodePoint(c);
            c = read();
        }
        return sb.toString();
    }

    static boolean isWhiteSpace(int c) {
        return c >= 0 && c <= 32;
    }

    public int nextInt() {
        int c = read();
        while (isWhiteSpace(c)) {
            c = read();
        }
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int ret = 0;
        while (c >= 0 && !isWhiteSpace(c)) {
            if (c < '0' || c > '9') {
                throw new NumberFormatException("digit expected " + (char) c
                        + " found");
            }
            ret = ret * 10 + c - '0';
            c = read();
        }
        return ret * sgn;
    }

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

    public String readLine() {
        try {
            return super.readLine();
        } catch (IOException e) {
            return null;
        }
    }

    }

class FastPrinter extends PrintWriter {

    public FastPrinter(OutputStream out) {
        super(out);
    }

    public FastPrinter(Writer out) {
        super(out);
    }


}