Educational DP Contest AtCoder M - Candies

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Points: 12
Time limit: 1.0s
Memory limit: 1G

Problem type

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

They have decided to share K candies among themselves. Here, for each i (1 \le i \le 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 \le N \le 100
  • 0 \le K \le 10^5
  • 0 \le a_i \le K

Input Specification

The first line will contain 2 space separated integers N and K.

The next line will contain N integers, a_1, a_2, \dots, a_N.

Output Specification

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

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

Sample Input 1

3 4
1 2 3

Sample Output 1

5

Explanation for Sample 1

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

Explanation for Sample 2

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

Sample Input 3

2 0
0 0

Sample Output 3

1

Explanation for Sample 3

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

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