## Candies

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Points: 12 (partial)
Time limit: 1.0s
Memory limit: 512M

Problem type
Allowed languages
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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 contact Rimuru or Ninjaclasher on slack.

There are children, numbered .

They have decided to share candies among themselves. Here, for each , Child must receive between and candies (inclusive). Also, no candies should be left over.

Find the number of ways for them to share candies, modulo . 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.

#### Input Specification

The first line will contain 2 space separated integers and .

The next line will contain integers, .

#### Output Specification

Print the number of ways for the children to share candies, modulo .

Note: Be sure to print the answer modulo .

#### 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:

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

#### Explanation For Sample 3

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

#### Sample Input 4

4 100000
100000 100000 100000 100000

#### Sample Output 4

665683269