Problem:
Score : 100 points

Problem Statement

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.

Sample Input 1

3 4
1 2 3

Sample Output 1

5

There are five ways for the children to share candies, as follows:

(0, 1, 3)

(0, 2, 2)

(1, 0, 3)

(1, 1, 2)

(1, 2, 1)

Here, in each sequence, the i-th element represents the number of candies that Child i receives.

Sample Input 2

1 10
9

Sample Output 2

0

There may be no ways for the children to share candies.

Sample Input 3

2 0
0 0

Sample Output 3

1

There is one way for the children to share candies, as follows:

(0, 0)

Sample Input 4

4 100000
100000 100000 100000 100000

Sample Output 4

665683269

Be sure to print the answer modulo 10^9 + 7.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

import java.io.*;
import java.math.BigInteger;

public class Main {
	FastScanner in;
	PrintWriter out;
	boolean systemIO = true;

	public long pow(long x, long p, long mod) {
		if (p <= 0) {
			return 1;
		}
		long th = pow(x, p / 2, mod);
		th *= th;
		th %= mod;
		if (p % 2 == 1) {
			th *= x;
		}
		return th;
	}

	public class Fraction implements Comparable<Fraction> {
		long x;
		long y;

		public Fraction(long x, long y) {
			this.x = x;
			this.y = y;
		}

		public void norm() {
			long gcd = gcd(x, y);
			x /= gcd;
			y /= gcd;
		}

		@Override
		public int compareTo(Fraction o) {
			if (x > o.x) {
				return 1;
			}
			if (x < o.x) {
				return -1;
			}
			if (y > o.y) {
				return 1;
			}
			if (y < o.y) {
				return -1;
			}
			return 0;
		}
	}

	public Fraction sum(Fraction a, Fraction b) {
		Fraction c = new Fraction(a.x * b.y + a.y * b.x, a.y * b.y);
		c.norm();
		return c;
	}

	public long gcd(long x, long y) {
		if (y == 0) {
			return x;
		}
		if (x == 0) {
			return y;
		}
		return gcd(y, x % y);
	}

	public class Pair implements Comparable<Pair> {
		long x;
		long y;

		public Pair(long x, long y) {
			this.x = x;
			this.y = y;
		}

		@Override
		public int compareTo(Pair o) {
			// if (x != o.x) {
			// return x - o.x;
			// }
			// return y - o.y;
			return 0;
		}
	}

	// public class Vertex {
	// Vertex father;
	// Vertex l;
	// Vertex r;
	// int sz;
	// long y;
	// long x;
	// int time;
	// int mintime;
	// int value;
	//
	// public Vertex(Vertex father, Vertex l, Vertex r, int sz, long y, long x, int
	// time, int mintime, int value) {
	// this.father = father;
	// this.l = l;
	// this.r = r;
	// this.sz = sz;
	// this.y = y;
	// this.x = x;
	// this.time = time;
	// this.mintime = mintime;
	// this.value = value;
	// }
	//
	// public Vertex(long x, int time, int value) {
	// this.father = null;
	// this.l = null;
	// this.r = null;
	// this.sz = 1;
	// this.y = random.nextLong();
	// this.x = x;
	// this.time = time;
	// this.mintime = time;
	// this.value = value;
	// }
	//
	// public void update() {
	// sz = 1;
	// mintime = time;
	// if (l != null) {
	// sz += l.sz;
	// mintime = Math.min(time, mintime);
	// }
	// if (r != null) {
	// sz += r.sz;
	// mintime = Math.min(time, mintime);
	// }
	// }
	// }
	//
	// public void add0(Vertex v, Vertex v1, Vertex father) {
	// if (v == null) {
	// v1.father = father;
	// father.r = v1;
	// father.update();
	// return;
	// }
	// if (v.y >= v1.y) {
	// add0(v.r, v1, v);
	// father.update();
	// return;
	// }
	// father.r = v1;
	// v1.father = father;
	// v.father = v1;
	// v1.l = v;
	// v1.update();
	// father.update();
	// }
	//
	// public Vertex pop(Vertex v, Vertex father, int h) {
	// if (v.l == null) {
	// if (h == 0) {
	// father.r = v.r;
	// } else {
	// father.l = v.r;
	// }
	// if (v.r != null) {
	// v.r.father = father;
	// v.r.update();
	// }
	// father.update();
	// v.father = null;
	// v.r = null;
	// v.update();
	// return v;
	// }
	// Vertex ans = pop(v.l, v, h + 1);
	// father.update();
	// return ans;
	// }
	//
	// public void cut(Vertex rl, Vertex rr, Vertex v, int mint) {
	//
	// }
	//
	// public int push(Vertex v, Vertex v1, Vertex father, boolean rson, int szl) {
	//
	// }
	//
	// Vertex root0;

	// public class State implements Comparable<State> {
	// int[] a;
	//
	// public State(int[] a) {
	// this.a = a;
	// }
	//
	// @Override
	// public int compareTo(State o) {
	// for (int i = 0; i < a.length; i++) {
	// if (a[i] != o.a[i]) {
	// return a[i] - o.a[i];
	// }
	// }
	// return 0;
	// }
	// }

	long mod = 1000000007;

	public void solve() {
		int n = in.nextInt();
		int k = in.nextInt();
		long[] dp = new long[k + 1];
		dp[k] = 1;
		for (int i = 0; i < n; i++) {
			long[] dp1 = new long[k + 1];
			int a = in.nextInt();
			long sum = 0;
			for (int j = k; j >= 0; j--) {
				sum += dp[j];
				if (j + a + 1 <= k) {
					sum -= dp[j + a + 1];
				}
				sum = ((sum % mod) + mod) % mod;
				dp1[j] = sum;
			}
			dp = dp1;
		}
		out.print(dp[0]);
	}

	public void run() {
		try {
			if (systemIO) {
				in = new FastScanner(System.in);
				out = new PrintWriter(System.out);
			} else {
				in = new FastScanner(new File("input.txt"));
				out = new PrintWriter(new File("output.txt"));
			}
			solve();

			out.close();
		} catch (IOException e) {
			e.printStackTrace();
		}
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		FastScanner(File f) {
			try {
				br = new BufferedReader(new FileReader(f));
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
		}

		FastScanner(InputStream f) {
			br = new BufferedReader(new InputStreamReader(f));
		}

		String nextLine() {
			try {
				return br.readLine();
			} catch (IOException e) {
				return null;
			}
		}

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

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

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

		double nextDouble() {
			return Double.parseDouble(next());
		}

	}

	// AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
	public static void main(String[] arg) {
		new Main().run();
	}
}