CF392C.Yet Another Number Sequence

普及/提高-

通过率：0%

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题目描述

Everyone knows what the Fibonacci sequence is. This sequence can be defined by the recurrence relation:

F_{1}=1,F_{2}=2,F_{i}=F_{i-1}+F_{i-2} (i>2). We'll define a new number sequence $A_{i}(k)$ by the formula:

$A_{i}(k)=F_{i}×i^{k} (i>=1).$ In this problem, your task is to calculate the following sum: $A_{1}(k)+A_{2}(k)+...+A_{n}(k)$ . The answer can be very large, so print it modulo $1000000007$ $(10^{9}+7)$ .

输入格式

The first line contains two space-separated integers $n$ , $k$ $(1<=n<=10^{17}; 1<=k<=40)$ .

输出格式

Print a single integer — the sum of the first $n$ elements of the sequence $A_{i}(k)$ modulo $1000000007$ $(10^{9}+7)$ .

输入输出样例

输入#1
```
1 1
```
输出#1
```
1
```
输入#2
```
4 1
```
输出#2
```
34
```
输入#3
```
5 2
```
输出#3
```
316
```
输入#4
```
7 4
```
输出#4
```
73825
```

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