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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

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

    static class MCandies {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            Numbers number = new Numbers(1000000007);
            int n = in.nextInt(), k = in.nextInt();
            int[] a = new int[n + 1];
            long[][] dp = new long[n + 5][k + 5];

            for (int i = 1; i <= n; i++) a[i] = in.nextInt();
            dp[0][0] = 1;
            for (int i = 1; i <= n; i++) {
                for (int j = 0; j <= k; j++) {
                    if (j > 0) dp[i][j] = number.add(dp[i][j], dp[i][j - 1]);
                    int x = Math.max(0, j - a[i]);
                    if (x == 0) dp[i][j] = number.add(dp[i][j], dp[i - 1][j]);
                    else {
                        long num = number.sub(dp[i - 1][j], dp[i - 1][x - 1]);
                        dp[i][j] = number.add(dp[i][j], num);
                    }
                }
            }
            out.println(dp[n][k]);
        }

    }

    static class Numbers {
        public long mod;

        public Numbers(long MOD) {
            mod = MOD;
        }

        public long add(long a, long b) {
            a += b;
            if (a >= mod) a -= mod;
            return a;
        }

        public long sub(long a, long b) {
            a -= b;
            if (a < 0) a += mod;
            return a;
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}

