These problems are from the AtCoder DP contest, and were transferred onto DMOJ. All problem statements were made by several AtCoder users. As there is no access to the test data, all data is randomly generated. If there are issues with the statement or data, please open a ticket by clicking the "Report an issue" button at the bottom of the page.
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.
- All values in input are integers.
- ~1 \le N \le 100~
- ~0 \le K \le 10^5~
- ~0 \le a_i \le K~
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~.
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
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
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
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