Extended Fibonacci

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Points: 10 (partial)
Time limit: 2.0s
Memory limit: 256M

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Problem type

Let

\displaystyle 
f(x) = \begin{cases} a_1f(x-1) + a_2f(x-2) + \ldots + a_Nf(x-N) & \text{if } x > N \\ 1 & \text{if } x \le N \end{cases}

Given N, Z and a, print f(Z) \bmod 10^9 + 7.

Input Specification

The first line will contain two integers, N, Z\ (1 \le N \le 10, 1 \le Z \le 10^5).

The second line will contain N integers, a_1, a_2, \ldots, a_N\ (1 \le a_i \le 10^6).

Output Specification

Print f(Z) \bmod 10^9+7.

Subtasks

Subtask 1 [20%]

N = 2, a_i = 1, Z \le 20

Subtask 2 [30%]

N = 2, a_i = 1

Subtask 3 [50%]

No further constraints.

Sample Input 1

2 5
1 1

Sample Output 1

5

Sample Input 2 (not in pretests)

6 90000
4 2 29 5 1 10

Sample Output 2

408918679

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