Inaho IX

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Points: 25 (partial)
Time limit: 0.6s
Memory limit: 64M

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Inaho is given a function:

\displaystyle 
f(x) = \begin{cases} a_1 f(x-1) + a_2 f(x-2) + \dots + a_N f(x-N) & \text{if } x > N \\ 1 & \text{if } x \le N \end{cases}

Given N, Z and a, Inaho wants you to 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 < 10^{10\,000}).

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

Output Specification

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

Subtasks

Subtask 1 [10%]

Z < 10^5

Subtask 2 [30%]

Z < 10^{18}

Subtask 3 [60%]

No further constraints.

Sample Input 1

2 5
1 1

Sample Output 1

5

Sample Input 2

6 90000
4 2 29 5 1 10

Sample Output 2

408918679

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