There are N children, numbered 1, 2, \ldots, N.

They have decided to share K candies among themselves. Here, for each i (1 \leq i \leq N), Child i must receive between 0 and a_i candies (inclusive). Also, no candies should be left over.

Find the number of ways for them to share candies, modulo 10^9 + 7. Here, two ways are said to be different when there exists a child who receives a different number of candies.

Constraints

* All values in input are integers.
* 1 \leq N \leq 100
* 0 \leq K \leq 10^5
* 0 \leq a_i \leq K

Input

Input is given from Standard Input in the following format:


N K
a_1 a_2 \ldots a_N


Output

Print the number of ways for the children to share candies, modulo 10^9 + 7.

Examples

Input

3 4
1 2 3


Output

5


Input

1 10
9


Output

0


Input

2 0
0 0


Output

1


Input

4 100000
100000 100000 100000 100000


Output

665683269
import java.io.*;
import java.util.*;
import java.lang.*;


public class Main implements Runnable {
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

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

        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 String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt() {
            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 nextLong() {
            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 double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
    public static void main(String args[]) throws Exception {
        new Thread(null, new Main(),"Main",1<<26).start();
    }

    static long gcd(long a,long b){ if(b==0)return a;return gcd(b,a%b); }
    static long modPow(long a,long p,long m){ if(a==1)return 1;long ans=1;while (p>0){ if(p%2==1)ans=(ans*a)%m;a=(a*a)%m;p>>=1; }return ans; }
    static long modInv(long a,long m){return modPow(a,m-2,m);}
    static long sol_x,sol_y,gcd_a_b;
    static void extendedEuclid(long a,long b){ if(b==0){gcd_a_b=a;sol_x=1;sol_y=0; } else{ extendedEuclid(b,a%b);long temp = sol_x;sol_x=sol_y;sol_y = temp - (a/b)*sol_y; } }
    static class Bhavansort{ Random random;Bhavansort(int a[]){ randomArray(a); sort(a);}Bhavansort(long a[]){ randomArray(a); sort(a);}static int[] sort(int a[]){ Arrays.sort(a);return a;}static long[] sort(long a[]){ Arrays.sort(a);return a; }void randomArray(long a[]){ int n=a.length;for(int i=0;i<n;i++){ int p=random.nextInt(n)%n;long tm=a[i];a[i]=a[p];a[p]=tm; } }void randomArray(int a[]){ int n=a.length;for(int i=0;i<n;i++){ int p=random.nextInt(n)%n;int tm=a[i];a[i]=a[p];a[p]=tm; } }}



    public void run() {
        InputReader sc = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);


        int n=sc.nextInt();
        int k=sc.nextInt();
        int a[]=new int[n+1];
        for (int i = 1; i <n+1 ; i++) {
            a[i]=sc.nextInt();
        }

        long dp[][]=new long[n+1][k+1];
        for (int i = 0; i <n+1 ; i++) {
            dp[i][0]=1;
        }
        long pre[][]=new long[n+1][k+1];
        Arrays.fill(pre[0],1);
        for (int i = 1; i <n+1 ; i++) {
            for (int j = 1; j <k+1 ; j++) {
                dp[i][j]=(dp[i-1][j]+f(pre,i-1,j-Math.min(a[i],j),j-1))%1000000007;
            }
            pre[i][0]=1;
            for (int j = 1; j <k+1 ; j++) {
                pre[i][j]=(pre[i][j-1]+dp[i][j])%1000000007;
            }
        }


        out.println(dp[n][k]);

        out.close();
    }

    long f(long pre[][],int i,int l,int r){
        if(l==0){
            return pre[i][r]%1000000007;
        }
        else{
            return (pre[i][r]-pre[i][l-1]+1000000007)%1000000007;
        }
    }



}