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.awt.*;
import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;
import java.util.List;

import static java.lang.Math.max;
import static java.lang.Math.min;


public class E implements Runnable{

    // SOLUTION!!!
    // HACK ME PLEASE IF YOU CAN!!!
    // PLEASE!!!
    // PLEASE!!!
    // PLEASE!!!

    private final static Random rnd = new Random();
    private final static String fileName = "";

    final static long MODULO = 1000 * 1000 * 1000 + 7;

    long inverseNMinus1Factorial;

    private void solve() {
        int n = readInt();
        long s = readLong();

        long[] f = readLongArray(n);

        Map<Long, Long> coeffs = new HashMap<>();
        coeffs.put(0L, 1L);

        class Pair {
            long power, coeff;

            public Pair(long power, long coeff) {
                this.power = power;
                this.coeff = coeff;
            }
        }

        for (long size : f) {
            List<Pair> coeffEntries = new ArrayList<>();
            for (Map.Entry<Long, Long> coeffEntry : coeffs.entrySet()) {
                long power = coeffEntry.getKey();
                long coeff = coeffEntry.getValue();

                long nextPower = power + size + 1;
                coeffEntries.add(
                    new Pair(
                        nextPower, -coeff
                    )
                );
            }

            for (Pair coeffEntry : coeffEntries) {
                coeffs.put(coeffEntry.power,
                        add(coeffs.getOrDefault(coeffEntry.power, 0L), coeffEntry.coeff)
                );
            }
        }

        long nMinus1Factorial = multSequence(1, n - 1);
        this.inverseNMinus1Factorial = inverse(nMinus1Factorial);

        long answer = 0;
        for (Map.Entry<Long, Long> coeffEntry : coeffs.entrySet()) {
            long power = coeffEntry.getKey();
            long coeff = coeffEntry.getValue();

            if (s >= power) {
                long need = s - power;
                answer = add(answer, mult(binom(n + need - 1, need), coeff));
            }
        }

        out.println(answer);
    }

    long multSequence(long start, long end) {
        long res = 1;
        for (long i = start; i <= end; ++i) {
            res = mult(res, i);
        }

        return res;
    }

    long inverse(long x) {
        return binpow(x, MODULO - 2);
    }

    long binpow(long base, long power) {
        if (power == 0) return 1;

        if ((power & 1) == 0) {
            long half = binpow(base, power >> 1);
            return mult(half, half);
        } else {
            long prev = binpow(base, power - 1);
            return mult(prev, base);
        }
    }

    long binom(long n, long k) {
        return mult(
                multSequence(k + 1, n),
                inverseNMinus1Factorial
        );
    }

    long add(long a, long b) {
        return ((a % MODULO + b % MODULO) % MODULO + MODULO) % MODULO;
    }

    long mult(long a, long b) {
        return (a % MODULO) * (b % MODULO) % MODULO;
    }

    /////////////////////////////////////////////////////////////////////

    private final static boolean FIRST_INPUT_STRING = false;
    private final static boolean MULTIPLE_TESTS = true;
    private final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;

    private final static int MAX_STACK_SIZE = 128;

    private final static boolean OPTIMIZE_READ_NUMBERS = true;

    /////////////////////////////////////////////////////////////////////

    public void run(){
        try{
            timeInit();
            Locale.setDefault(Locale.US);

            init();

            if (ONLINE_JUDGE) {
                solve();
            } else {
                do {
                    try {
                        timeInit();
                        solve();
                        time();

                        out.println();
                    } catch (NumberFormatException e) {
                        break;
                    } catch (NullPointerException e) {
                        if (FIRST_INPUT_STRING) break;
                        else throw e;
                    }
                } while (MULTIPLE_TESTS);
            }

            out.close();
            time();
        }catch (Exception e){
            e.printStackTrace(System.err);
            System.exit(-1);
        }
    }

    /////////////////////////////////////////////////////////////////////

    private BufferedReader in;
    private OutputWriter out;
    private StringTokenizer tok = new StringTokenizer("");

    public static void main(String[] args){
        new Thread(null, new E(), "", MAX_STACK_SIZE * (1L << 20)).start();
    }

    /////////////////////////////////////////////////////////////////////

    private void init() throws FileNotFoundException{
        Locale.setDefault(Locale.US);

        if (ONLINE_JUDGE){
            if (fileName.isEmpty()) {
                in = new BufferedReader(new InputStreamReader(System.in));
                out = new OutputWriter(System.out);
            } else {
                in = new BufferedReader(new FileReader(fileName + ".in"));
                out = new OutputWriter(fileName + ".out");
            }
        }else{
            in = new BufferedReader(new FileReader("input.txt"));
            out = new OutputWriter("output.txt");
        }
    }

    ////////////////////////////////////////////////////////////////

    private long timeBegin;

    private void timeInit() {
        this.timeBegin = System.currentTimeMillis();
    }

    private void time(){
        long timeEnd = System.currentTimeMillis();
        System.err.println("Time = " + (timeEnd - timeBegin));
    }

    private void debug(Object... objects){
        if (ONLINE_JUDGE){
            for (Object o: objects){
                System.err.println(o.toString());
            }
        }
    }

    /////////////////////////////////////////////////////////////////////

    private String delim = " ";

    private String readLine() {
        try {
            return in.readLine();
        } catch (IOException e) {
            throw new RuntimeIOException(e);
        }
    }

    private String readString() {
        try {
            while(!tok.hasMoreTokens()){
                tok = new StringTokenizer(readLine());
            }

            return tok.nextToken(delim);
        } catch (NullPointerException e) {
            return null;
        }
    }

    /////////////////////////////////////////////////////////////////

    private final char NOT_A_SYMBOL = '\0';

    private char readChar() {
        try {
            int intValue = in.read();

            if (intValue == -1){
                return NOT_A_SYMBOL;
            }

            return (char) intValue;
        } catch (IOException e) {
            throw new RuntimeIOException(e);
        }
    }

    private char[] readCharArray() {
        return readLine().toCharArray();
    }

    private char[][] readCharField(int rowsCount) {
        char[][] field = new char[rowsCount][];
        for (int row = 0; row < rowsCount; ++row) {
            field[row] = readCharArray();
        }

        return field;
    }

    /////////////////////////////////////////////////////////////////

    private long optimizedReadLong() {
        int sign = 1;
        long result = 0;
        boolean started = false;
        while (true) {
            try {
                int j = in.read();
                if (-1 == j) {
                    if (started) return sign * result;
                    throw new NumberFormatException();
                }

                if (j == '-') {
                    if (started) throw new NumberFormatException();
                    sign = -sign;
                }

                if ('0' <= j && j <= '9') {
                    result = result * 10 + j - '0';
                    started = true;
                } else if (started) {
                    return sign * result;
                }
            } catch (IOException e) {
                throw new RuntimeIOException(e);
            }
        }
    }

    private int readInt() {

        if (!OPTIMIZE_READ_NUMBERS) {
            return Integer.parseInt(readString());
        } else {
            return (int) optimizedReadLong();
        }
    }

    private int[] readIntArray(int size) {
        int[] array = new int[size];

        for (int index = 0; index < size; ++index){
            array[index] = readInt();
        }

        return array;
    }

    private int[] readSortedIntArray(int size) {
        Integer[] array = new Integer[size];

        for (int index = 0; index < size; ++index) {
            array[index] = readInt();
        }
        Arrays.sort(array);

        int[] sortedArray = new int[size];
        for (int index = 0; index < size; ++index) {
            sortedArray[index] = array[index];
        }

        return sortedArray;
    }

    private int[] readIntArrayWithDecrease(int size) {
        int[] array = readIntArray(size);

        for (int i = 0; i < size; ++i) {
            array[i]--;
        }

        return array;
    }

    ///////////////////////////////////////////////////////////////////

    private int[][] readIntMatrix(int rowsCount, int columnsCount) {
        int[][] matrix = new int[rowsCount][];

        for (int rowIndex = 0; rowIndex < rowsCount; ++rowIndex) {
            matrix[rowIndex] = readIntArray(columnsCount);
        }

        return matrix;
    }

    private int[][] readIntMatrixWithDecrease(int rowsCount, int columnsCount) {
        int[][] matrix = new int[rowsCount][];

        for (int rowIndex = 0; rowIndex < rowsCount; ++rowIndex) {
            matrix[rowIndex] = readIntArrayWithDecrease(columnsCount);
        }

        return matrix;
    }

    ///////////////////////////////////////////////////////////////////

    private long readLong() {
        if (!OPTIMIZE_READ_NUMBERS) {
            return Long.parseLong(readString());
        } else {
            return optimizedReadLong();
        }
    }

    private long[] readLongArray(int size) {
        long[] array = new long[size];

        for (int index = 0; index < size; ++index){
            array[index] = readLong();
        }

        return array;
    }

    ////////////////////////////////////////////////////////////////////

    private double readDouble() {
        return Double.parseDouble(readString());
    }

    private double[] readDoubleArray(int size) {
        double[] array = new double[size];

        for (int index = 0; index < size; ++index){
            array[index] = readDouble();
        }

        return array;
    }

    ////////////////////////////////////////////////////////////////////

    private BigInteger readBigInteger() {
        return new BigInteger(readString());
    }

    private BigDecimal readBigDecimal() {
        return new BigDecimal(readString());
    }

    /////////////////////////////////////////////////////////////////////

    private Point readPoint() {
        int x = readInt();
        int y = readInt();
        return new Point(x, y);
    }

    private Point[] readPointArray(int size) {
        Point[] array = new Point[size];

        for (int index = 0; index < size; ++index){
            array[index] = readPoint();
        }

        return array;
    }

    /////////////////////////////////////////////////////////////////////

    @Deprecated
    private List<Integer>[] readGraph(int vertexNumber, int edgeNumber) {
        @SuppressWarnings("unchecked")
        List<Integer>[] graph = new List[vertexNumber];

        for (int index = 0; index < vertexNumber; ++index){
            graph[index] = new ArrayList<>();
        }

        while (edgeNumber-- > 0){
            int from = readInt() - 1;
            int to = readInt() - 1;

            graph[from].add(to);
            graph[to].add(from);
        }

        return graph;
    }

    private static class GraphBuilder {

        final int size;
        final List<Integer>[] edges;

        static GraphBuilder createInstance(int size) {
            List<Integer>[] edges = new List[size];
            for (int v = 0; v < size; ++v) {
                edges[v] = new ArrayList<>();
            }

            return new GraphBuilder(edges);
        }

        private GraphBuilder(List<Integer>[] edges) {
            this.size = edges.length;
            this.edges = edges;
        }

        public void addEdge(int from, int to) {
            addDirectedEdge(from, to);
            addDirectedEdge(to, from);
        }

        public void addDirectedEdge(int from, int to) {
            edges[from].add(to);
        }

        public int[][] build() {
            int[][] graph = new int[size][];
            for (int v = 0; v < size; ++v) {
                List<Integer> vEdges = edges[v];
                graph[v] = castInt(vEdges);
            }

            return graph;
        }
    }

    /////////////////////////////////////////////////////////////////////

    private static class IntIndexPair {

        static Comparator<IntIndexPair> increaseComparator = new Comparator<E.IntIndexPair>() {

            @Override
            public int compare(E.IntIndexPair indexPair1, E.IntIndexPair indexPair2) {
                int value1 = indexPair1.value;
                int value2 = indexPair2.value;

                if (value1 != value2) return value1 - value2;

                int index1 = indexPair1.index;
                int index2 = indexPair2.index;

                return index1 - index2;
            }
        };

        static Comparator<IntIndexPair> decreaseComparator = new Comparator<E.IntIndexPair>() {

            @Override
            public int compare(E.IntIndexPair indexPair1, E.IntIndexPair indexPair2) {
                int value1 = indexPair1.value;
                int value2 = indexPair2.value;

                if (value1 != value2) return -(value1 - value2);

                int index1 = indexPair1.index;
                int index2 = indexPair2.index;

                return index1 - index2;
            }
        };

        int value, index;

        IntIndexPair(int value, int index) {
            super();
            this.value = value;
            this.index = index;
        }

        int getRealIndex() {
            return index + 1;
        }
    }

    private IntIndexPair[] readIntIndexArray(int size) {
        IntIndexPair[] array = new IntIndexPair[size];

        for (int index = 0; index < size; ++index) {
            array[index] = new IntIndexPair(readInt(), index);
        }

        return array;
    }

    /////////////////////////////////////////////////////////////////////

    private static class OutputWriter extends PrintWriter {

        final int DEFAULT_PRECISION = 12;

        private int precision;
        private String format, formatWithSpace;

        {
            precision = DEFAULT_PRECISION;

            format = createFormat(precision);
            formatWithSpace = format + " ";
        }

        OutputWriter(OutputStream out) {
            super(out);
        }

        OutputWriter(String fileName) throws FileNotFoundException {
            super(fileName);
        }

        int getPrecision() {
            return precision;
        }

        void setPrecision(int precision) {
            precision = max(0, precision);
            this.precision = precision;

            format = createFormat(precision);
            formatWithSpace = format + " ";
        }

        String createFormat(int precision){
            return "%." + precision + "f";
        }

        @Override
        public void print(double d){
            printf(format, d);
        }

        void printWithSpace(double d){
            printf(formatWithSpace, d);
        }

        void printAll(double...d){
            for (int i = 0; i < d.length - 1; ++i){
                printWithSpace(d[i]);
            }

            print(d[d.length - 1]);
        }

        @Override
        public void println(double d){
            printlnAll(d);
        }

        void printlnAll(double... d){
            printAll(d);
            println();
        }
    }

    /////////////////////////////////////////////////////////////////////

    private static class RuntimeIOException extends RuntimeException {

        /**
         *
         */
        private static final long serialVersionUID = -6463830523020118289L;

        RuntimeIOException(Throwable cause) {
            super(cause);
        }
    }

    /////////////////////////////////////////////////////////////////////
    //////////////// Some useful constants and functions ////////////////
    /////////////////////////////////////////////////////////////////////

    private static final int[][] steps = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};
    private static final int[][] steps8 = {
            {-1, 0}, {1, 0}, {0, -1}, {0, 1},
            {-1, -1}, {1, 1}, {1, -1}, {-1, 1}
    };

    private static boolean checkCell(int row, int rowsCount, int column, int columnsCount) {
        return checkIndex(row, rowsCount) && checkIndex(column, columnsCount);
    }

    private static boolean checkIndex(int index, int lim){
        return (0 <= index && index < lim);
    }

    /////////////////////////////////////////////////////////////////////

    private static boolean checkBit(int mask, int bit){
        return (mask & (1 << bit)) != 0;
    }
    private static boolean checkBit(long mask, int bit){
        return (mask & (1L << bit)) != 0;
    }

    /////////////////////////////////////////////////////////////////////

    private static long getSum(int[] array) {
        long sum = 0;
        for (int value: array) {
            sum += value;
        }

        return sum;
    }

    private static Point getMinMax(int[] array) {
        int min = array[0];
        int max = array[0];

        for (int index = 0, size = array.length; index < size; ++index, ++index) {
            int value = array[index];

            if (index == size - 1) {
                min = min(min, value);
                max = max(max, value);
            } else {
                int otherValue = array[index + 1];

                if (value <= otherValue) {
                    min = min(min, value);
                    max = max(max, otherValue);
                } else {
                    min = min(min, otherValue);
                    max = max(max, value);
                }
            }
        }

        return new Point(min, max);
    }

    /////////////////////////////////////////////////////////////////////

    private static int[] getPrimes(int n) {
        boolean[] used = new boolean[n];
        used[0] = used[1] = true;

        int size = 0;
        for (int i = 2; i < n; ++i) {
            if (!used[i]) {
                ++size;
                for (int j = 2 * i; j < n; j += i) {
                    used[j] = true;
                }
            }
        }

        int[] primes = new int[size];
        for (int i = 0, cur = 0; i < n; ++i) {
            if (!used[i]) {
                primes[cur++] = i;
            }
        }

        return primes;
    }

    /////////////////////////////////////////////////////////////////////

    private static long lcm(long a, long b) {
        return a / gcd(a, b) * b;
    }

    private static long gcd(long a, long b) {
        return (a == 0 ? b : gcd(b % a, a));
    }

    /////////////////////////////////////////////////////////////////////

    private static class MultiSet<ValueType> {

        public static <ValueType> MultiSet<ValueType> createMultiSet() {
            Map<ValueType, Integer> multiset = new HashMap<>();
            return new MultiSet<>(multiset);
        }

        private final Map<ValueType, Integer> multiset;
        private int size;

        public MultiSet(Map<ValueType, Integer> multiset) {
            this.multiset = multiset;
            this.size = 0;
        }

        public int size() {
            return size;
        }

        public void inc(ValueType value) {
            int count = get(value);
            multiset.put(value, count + 1);

            ++size;
        }

        public void dec(ValueType value) {
            int count = get(value);
            if (count == 0) return;

            if (count == 1) multiset.remove(value);
            else multiset.put(value, count - 1);

            --size;
        }

        public int get(ValueType value) {
            Integer count = multiset.get(value);
            return (count == null ? 0 : count);
        }
    }

    /////////////////////////////////////////////////////////////////////

    private static class IdMap<KeyType> extends HashMap<KeyType, Integer> {

        /**
         *
         */
        private static final long serialVersionUID = -3793737771950984481L;

        public IdMap() {
            super();
        }

        int getId(KeyType key) {
            Integer id = super.get(key);
            if (id == null) {
                super.put(key, id = size());
            }

            return id;
        }
    }

    /////////////////////////////////////////////////////////////////////

    private static int[] castInt(List<Integer> list) {
        int[] array = new int[list.size()];
        for (int i = 0; i < array.length; ++i) {
            array[i] = list.get(i);
        }

        return array;
    }

    private static long[] castLong(List<Long> list) {
        long[] array = new long[list.size()];
        for (int i = 0; i < array.length; ++i) {
            array[i] = list.get(i);
        }

        return array;
    }
}