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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

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

    static class TaskE {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            try {
                int n = in.readInt();
                long s = in.readLong();
                long[] f = in.readLongArray(n);
                MiscUtils.increaseByOne(f);
                long res = 0;
                for (int mask = 0; mask < (1 << n); mask++) {
                    long k = 0;
                    int sign = 1;
                    for (int i = 0; i < n; i++) {
                        if (((mask >> i) & 1) == 1) {
                            k += f[i];
                            sign *= -1;
                        }
                    }
                    if (k > s) {
                        continue;
                    }
                    long rem = s - k, coef = IntegerUtils.binomialCoefficient(rem + n - 1, rem, MiscUtils.MOD7);
                    res = IntegerUtils.trueMod(res + sign * coef, MiscUtils.MOD7);
                }
                out.printLine(res);
            } catch (Exception e) {
                e.printStackTrace();
            }
        }

    }

    static class MiscUtils {
        public static final int MOD7 = (int) (1e9 + 7);

        public static void increaseByOne(long[]... arrays) {
            for (long[] array : arrays) {
                for (int i = 0; i < array.length; i++) {
                    array[i]++;
                }
            }
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public long[] readLongArray(int size) {
            long[] array = new long[size];
            for (int i = 0; i < size; i++) {
                array[i] = readLong();
            }
            return array;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long readLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void printLine(long i) {
            writer.println(i);
        }

    }

    static class IntegerUtils {
        private static long _x;
        private static long _y;

        public static long trueMod(long a, long b) {
            a %= b;
            a += b;
            a %= b;
            return a;
        }

        public static long factorial(int n, long mod) {
            long result = 1;
            for (int i = 2; i <= n; i++) {
                result = result * i % mod;
            }
            return result % mod;
        }

        public static long reverse(long number, long modulo) {
            extGcd(number, modulo);
            return trueMod(_x, modulo);
        }

        private static long extGcd(long a, long b) {
            if (a == 0) {
                _x = 0;
                _y = 1;
                return b;
            }
            long d = extGcd(b % a, a);
            long nx = _y - (b / a) * _x;
            //noinspection SuspiciousNameCombination
            _y = _x;
            _x = nx;
            return d;
        }

        public static long binomialCoefficient(long n, long m, long mod) {
            if (m < 0 || m > n) {
                return 0;
            }
            if (2 * m > n) {
                m = n - m;
            }
            long result = 1;
            for (long i = n - m + 1; i <= n; i++) {
                result = result * (i % mod) % mod;
            }
            return result * reverse(factorial((int) m, mod), mod) % mod;
        }

    }
}